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THE    CELEBRATED 


Steel  Squares 

MANUFACTURED    BY 

SARGENT   &    CO. 

/RE    THE     RECOq;^IZ;ED     ^TAfiDJ^Y{D^,     fAADZ    f^^^ 

UJMEXCELX-ED    jVIy^TEFJI/I-^  /ND   OJM    IJVIPr^OVEF 

]Vl/CHIJ^(ERY    OF   DEJ-ICATj:  /DJU^T/VlflJMT. 

NOJ\r£  GENUINE  UNLESS  STAMPED 


ALL    SUCH    SQUARES    FULLY    WARRANTED, 


FOR  SALE  BY  ALL  HARDWARE  DEALERS. 


"Decidedly  the  most  convenient  Square  for  the  operative 
workman  in  the  market." — Hodgson. 


r)i  A 


Steel  Squares 

AND    THEIR    USES. 


BEING    A    DESCRIPTION    OF    THE    VARIOUS   STEEL  SQUARES    AND   THEIR 
USES  IN  SOLVING  A  LARGE  NUMBER  OF  MECHANICAL  PROBLEMS  IN 

Constructive  Carpentry,  Joinery,  Sheet  Metal 
Work,  Cut  Stone  and  Brick  Work. 

ALSO    SHOWING     HOW    MANY    GEOMETRICAL    AND    OTHER     PROBLEMS 
MAY  BE   SOLVED  BY  THE  USE   OF  THE   STEEL  SQUARE. 

BY 

FRED.    T.    HODGSON, 
Editor  of  "  The  Builder  and  Woodworker.'' 

Author  of  "The  Carpenter's  Steel  Square  and  its  Uses  ;"    "The  Builder's 

Guide  and  Estimator's  Price  Book;"    •'Practical  Carpentry;  " 

"Stair  Building  Made  Easy;"  "Hand  Saws — Their  Carb 

AND  Use  ; "    "  Plaster,  How  to  Make  and  How  to 

Use;"  etc.,  etc. 

FULLY  ILLUSTRATED  WITH  NUMEROUS    ENGRAVINGS   AND   DIAGRAMS. 


NEW   YORK: 

THE  INDUSTRIAL  PUBLICATION  COMPANY. 

1890. 

GopyrigM,  Secured,  1890,  hy  John  Fhin. 


JtHrU 


Tif^ 


STEEL    SQUARES 


AND 


THEIR    USES. 


■^.A^IFLT     II. 


THIS    BOOK 

IS     DEDICATED     TO     MY     SON, 

FRED.    ALBERT    HODGSON, 

WHOSE  DEVOTION,  KINDLY   ASSISTANCE   AND   PLEASING  COMPANIONSHIP 

HAVE  MADE  THE  WRITING  OF  THIS   LITTLE  WORK 

A   LABOR   OF  PLEASURE. 

THE    AUTHOR. 


PREFACE, 


The  great  demand  for  the  first  volume  of  ''The  Steel 
Square  and  Its  Uses"  convinced  the  writer  that  a  second 
volume  on  the  same  subject  would  be  sure  to  meet  with  a  fair 
reception. 

The  150,000  readers  of  Vol.  I.  will  want  to  see  and  know 
more  of  what  may  be  done  by  the  aid  of  the  Steel  Square  and 
a  little  mental  effort. 

The  present  volume,  like  the  first,  contains  but  little  of 
bewildering  mathematics,  and  is  brought  down  as  near  to  the 
operative  workman's  standard  as  possible. 

Perhaps  many  readers  of  this  book  will  find  between  its 
covers  some  things  they  have  known  for  years  or  have  seen 
employed  by  some  fellow  workmen  ;  they  will,  however,  find 
many  things  and  problems  they  have  never  seen,  and  some 
little  ** dodges"  they  have  not  heard  of  before,  any  one  of 
which  will  be  worth  to  them  the  whole  price  paid  for  the  book. 
Indeed,  the  writer  considers  the  matter  and  illustrations  pre- 
sented in  this  work  of  much  more  importance  to  the  advanced 


PREFACE. 

workman  than  that  which  appeared  in  the  first,  and  feels 
assured  his  labors  on  The  Square  would  not  be  complete 
without  the  present  treatise. 

At  this  writing  (1890)  over  150,000  copies  of  the  first 
volume  have  been  sold,  and  the  demand  is  still  brisk,  thus 
showing  there  was  a  want  of  a  work  of  this  kind  ;  and  as  the 
first  volume  did  not  nearly  exhaust  the  subject,  it  became  the 
duty  of  the  author  to  supplement  it  with  the  present  one, 
which  it  is  thought  will  pretty  nearly  cover  the  ground. 

Never,  perhaps,  in  the  history  of  technical  literature  has  a 
work  exceeded  50,000  or  60,000  of  a  circulation,  and  it  is 
both  flattering  to  the  author  and  gratifying  to  the  publishers 
to  find  that  their  efforts  to  aid  the  workman  in  acquiring 
technical  knowledge  have  been  so  generously  appreciated. 
It  is  hoped  their  present  eff"orts  in  the  same  direction  will 
do  as  much  good  and  deserve  a  like  appreciation. 

THE  AUTHOR. 
New  York,  May,  1890. 


CONTENTS. 


PAGB 

Dedication. vii 

Preface .    ix 

Contents xi 

Preliminary 15 

Advice  to  Students 15 

Polygons 15 

Equal  and  Uni^qual  Squares 15 

Pentagons 16 

Scientific  way  of  forming  Pentagons 16 

Pentagons  by  the  "Square " 16 

Hexagon  Figure 17 

How  to  Construct  Hexagons 18 

Figure  of  Heptagon 18 

How  to  Construct  Heptagons 18 

Figure  of  Octagon 19 

To  Construct  Octagons 19 

To  Construct  an  Octagon  by  the  Square 19 

Advice  to  Young  Workmen 20 

Figure  of  Nonagon 20 

How  to  Construct  Nonagon  with  the   Square 20 

To  lay  off  Octagon  in  a  Square 21 

Figure  of  Square  and  Octagon 21 

Octagon  described  from  edge 21 


Xil  CONTENTS. 

PACK 

To  lay  off  Octagon  on  a  given  side 21 

Making  a  Square  stick  Octagonal 21 

To  find  the  side  of  an  Octagon  when  side  of  Square  is  given. ...  22 

When  the  side  of  an  Octagon  is  given,  to  find  the  square  width. .  22 

Figure  showing  application  of  Square  for  constructing  Octagon ...  22 

Octagonal  and  Hexagonal  Roofs 22 

Figure  of  Octagon  Roof. 23 

Side  Bevels  Octagonal  Roof 23 

Backing  Hips  for  Octagonal  Roofs 23 

Jack  Rafters  for  Octagonal  Roofs 23 

Hexagonal  Roof 24 

Hips  and  Jack  Rafters  for  Hexagonal  Roof 24 

Hexagonal  and  Octagonal  Boxes  or  Hoppers 24 

Cuts  and  Bevels  for  Octagonal  and  Hexagonal  Hoppers 25 

Figure  of  Hopper 25 

To  test  a  Square 25 

Diagram  of  Test 26 

How  to  find  the  centre  of  a  Circle  with  the  Square 26 

Figure  showing  method 26 

Three  points  not  in  a  straight  line  being  given,  to  find  the  centre 

of  a  circle  which  will  pass  through  them 26 

To  find  a  circle  equal  in  area  to  two  or  more  circles 27 

Diagram  showing  how  done 27 

Rule  applied  to  other  Figures 27 

To  find  the  .side  of  a  square  of  half  the  area  of  a  given  square  . .  28 

Equilateral  Triangle 28 

Figure  of  Equilateral  Triangle 28 

Bisecting  Angles  by  using  the  Square 29 

Two  Diagrams  showing  manner  of  Bisecting. 29 

Method  of  dividing  Angles 30 

Figure  with  Bisected  Angles 30 


CONTENTS.  Xlll 

PAGE 

Obtuse  and  Acute  Angles  Bisected 31 

Diagram  showing  method 31 

Method  of  finding  Angles 32 

Two  Diagrams 32 

Angles  of  30*^  and  60",  and  how  found 33 

Protractor  made  by  Square 33 

Tangent  Problem 34 

To  find  a  Tangent 35 

Good  for  Stair-builders 35 

Finding  a  lost  Centre 36 

Diagram  showing  how  found 37 

Practical  applications  of  rule 38 

Proportioning  Columns 39 

Method  illustrated 39 

Diagonal  Scale 41 

Diagram  of  Scale 42 

Scale  and  uses  explained. . , 43 

To  make  Flared  or  Splayed  Circular  Work 44 

Two  Diagrams  in  explanation 44 

Steel  Squares  generally 45 

The  No.  100  Square 46 

The  No.  200  Square 46 

The  Crenelated  Square 47 

Directions  for  using 48 

A  Combination  Square 49 

Seven  illustrations  of  Combination  Square 50 

Useful  applications  of  the  Steel  Square '  i 

Combination  Diagram 52 

Length  of  Chords 53 

Division  of  Circles 55 

Construction  of  Unequal  Squares. ,,,,.,.., 57 


Xiv  CONTENTS. 

PAGB 

Circumferences  of  Circles 59 

Degrees  and  Angles  obtained  by  using  the  Square 61 

Hip,  Valley,  Mansard  and  other  Roofs 62 

To  cut  a  Purlin  against  a  Valley  Rafter 63 

Another  method 64 

To  Timber  a  Hexagon  Roof 65 

Lines  for  Hip  Roofs 66 

Valley  Rafters  and  Cripples 67 

Rule  for  Valley  Rafters 67 

Pyramidal  Frame  Work 67 

Diagram  of  Battered  Frame 68 

Make  a  Pyramid 68 

Windmill  Frame 69 

Backing  Corner  Posts 70 

Two  Diagrams  of  Post  Bevels 70 

Mansard  and  French  Roofs 71 

Manner  of  making  Mansard  Roof 72 

Another  style  of  Mansard  Roof 73 

Another  form  of  Roof. 73 

Concerning  Hoppers 73 

Diagram  of  Roof 74 

Hopper  Lines 75 

A  Constant  Diagram 76 

Butt  Joints  for  Hoppers 7^ 

Mitres  for  Hoppers 7^ 

Hoppers  with  unequal  Flares 77 

Novel  method  of  cutting  Hopper  Joints 78 

Hexagonal  Hoppers 79 

Diagram  of  Hexagonal  Hopper Sc 


Steel    Squares 

AND    THEIR    USES. 


Preliminary. — Every  angle  or  cut  for  rafters,  hoppers, 
raking  mouldings  ,or  mitres,  is  some  angle  of  a  polygon  or 
right-angled  triangle ;  therefore  it  is  fitting  this  work  should 
open  with  rules  for  finding  the  inclination  of  sides,  construction 
and  angles  of  same.  It  is  thought  the  methods  shown  herewith 
will  prove  both  new  and  useful  to  many  mechanics,  and  will  be 
a  valuable  addition  to  the  literature  of  the  Steel  Square. 

The  student  is  earnestly  advised  to  construct  polygons  of 
all  sorts  by  the  usual  method,  then  make  a  table  of  the  figures 
required  to  construct  the  figures  and  find  the  angles.  The 
following  methods  will  give  an  idea  of  how  the  angles  and 
lines  may  be  found  by  using  the  steel  square. 

Polygons. — Polygons  are  nearly  as  much  used  in  the  con- 
structive arts  as  ellipses  or  circles,  and  I  think  it  quite  fitting 
to  begin  real  work  in  this  book  with  these  figures. 

A  square  figure  whose  sides  are  equal,  or  unequal,  as  the 
case  may  be,  if  all  the  angles  are  right,  requires  no  descrip- 
tion, as  every  workman  knows  how  to  construct  such  a  figure  ; 
§0  I  will   begin  by  showing  how  a  pentagon,  or  five-sided 


i6 


STEEL  SQUARES 


figure,  may  be  constructed.  There  are  several  methods  of 
forming  this  figure,  but  I  prefer  the  following  :  On  a  given 
line  let  A  B,  Fig.  i,  be  the  length  of  one  side  ;  divide  this 
into  two  equal  parts,  marking  it  as  at  2.  From  B  square  up  a 
line,  and  make  B  N  equal  to  A  B  ;  then  with  2  as  a  centre 
and  2  N  as  radius,  describe  the  arc,  cutting  the  line  A  B  at  3. 
Now  take  A  3  for  radius,  and  from  A  and  B  as  centres  make 


Fig.  I. 

the  intersections  at  D  ;  then  from  D,  with  a  radius  equal  to 
A  B,  describe  an  arc  as  shown  ;  then  using  A  and  B  for  centres, 
intersect  the  arc  in  E  and  C  ;  connect  these  points  together  with 
straight  lines,  and  the  pentagon  is  complete. 

This  is  a  scientific  way  of  forming  this  figure,  but  it  may  be 
obtained  much  easier  by  the  square. 

It  may  be  necessary  to  explain  that  in  regular  equal-sided 


AND      THEIR      USES. 


17 


polygons  the  angles  are  equal,  so  any  side  of  a  regular  polygon 
may  be  used  for  a  base  line.  Let  this  fact  be  remembered, 
as  it  is  important  the  student  should  keep  it  in  mind  when 
dealing  with  any  problem  connected  with  polygons,  where  the 
steel  square  is  used  :  By  a  careful  examination  of  Fig.  i  it  will 
be  seen  that  the  outer  edge  of  the  tongue  of  the  square  is  in  line 
with  one  side,  A  E,  of  the  pentagon,  measuring  down  below 
the  base  line,  A  B,  six  inches  ;  then  the  2 1  inch  mark  on  the 


outer  edge  of  the  square  will  also  touch  the  base  line,  A  B. 
This  position  of  the  square  then  gives  the  exact  inclination  of 
the  side  of  the  pentagon  with  the  base.  Now  if  we  reverse  the 
square  and  place  the  6  in.  mark  at  B,  and  the  21  in.  mark  on 
he  line  A  B,  we  get  three  sides  of  the  figure.  Now  make  the 
distance  from  A  to  E  the  same  as  A  B,  and  we  have  the  length 
ol  that  side.  Perform  the  same  operation  with  B  C.  Then 
using  A  E  and  B  C  as  base  lines,  we  can  form  the  figure  com- 


i8 


STEEL      SQUARES 


plete.  This  shows  how  any  pentagon  having  equal  sides  can 
be  formed  with  the  square.  The  method  of  obtaining  the 
mitres  or  cuts  suitable  for  cutting  joints  in  mouldings  and 
other  works,  for  this  and  all  other  polygons,  will  be  shown 
further  on. 

Now  remember  that  6  in.  on  the  tongue  and  21  in.  on  the 
blade  gives  the  proper  angle  for  forming  pentagons. 


Fig.  3- 

To  make  a  Hexagon,  Fig.  2,  take  seven  inches  on  the 
tongue  and  twelve  inches  on  the  blade,  and  apply  as  shown 
on  a  base  line  which  forms  a  square  around  the  figure. 

Fig.  3  shows  a  Heptagon,  or  seven-sided  figure,  and  the 
manner  in  which  it  is  obtained.  To  get  the  angle  as  shown, 
form  a  square  in  accordance  with  dimensions  required  ;  then 
inscribe  a  circle  as  shown  ;  then  place  the  square  as  repre- 
sented, using  the  base  line  of  the  outside  figure  having  the 


AND      THEIR      USES. 


19 


tongue  running  in  a  line  with  the  centre,  keeping  the  7  in. 
mark  on  the  base  line  ;  then  on  the  blade  the  14  in.  mark 
will  be  over  the  base  line.  Hence,  7  in.  on  the  tongue  and 
14  in.  on  the  blade  gives  the  figures  for  finding  the  lines  for  a 
heptagon. 

Perhaps  there  is  no  one  of  the  polygons  so  much  used  as 
the  octagon,  Fig.  4,  with  the  exception,  of  course,  of  the 
square  or  four-sided  figure.      In  consequence  of  this  fact,  I 


Fig.  4- 

think  it  necessary  to  say  more  of  it  than  of  the  other  polygons. 
An  octagon,  as  my  readers  know,  is  an  eight-sided  figure,  and 
may  be  obtained  by  many  different  methods,  among  which 
are  those  shown  at  Figs.  6,  7  and  8,  of  which  more  will  follow. 
In  Fig.  4  it  will  be  seen  that  the  figure  may  be  easily  formed 
by  using  the  square  as  shown.  Take  seven  inches  on  the 
tongue  and  seventeen  on  the  blade,  and  apply  on  the  base 
line,  and  the  angles  are  readily  obtained.     It  will  be  seen  that 


20  STEEL      SQUARES 

nearly  all  kinds  of  polygons  may  be  obtained  by  using  the 
square,  and  any  workman  may  discover  for  himself  the  figures 
on  the  square  to  apply  by  constructing  a  polygon  of  any  num- 
ber of  sides,  and  then  applying  the  square  in  such  a  manner 
as  to  understand  its  application  for  the  formation  of  any  similar 
figures. 

The  following,  which  relates  to  octagons  particularly,  will 
be  found  of  much  service  to  the  younger  workmen;  and  I 


Fig.  5- 

would  advise  them  to  master  all  these  little  "kinks,"  and  to 
procure  a  copy  of  the  first  part  of  the  work  on  this  subject, 
^nd  study  up  all  that  is  said  there  on  the  subject  of  polygons, 
and  I  am  sure  they  will  thank  me  for  bringing  the  matter  to 
their  notice. 

Fig.    5  exhibits  a  nonagon,   a  figure  having  nine  sides. 
It  is  but  seldom  used,  but  may  be  wanted  sometimes,  so  it  ig 


AND      THEIR      USES. 


21 


as  well  to  have  it  described.  Five  inches  on  the  tongue  and 
thirteen  inches  on  the  blade  will  give  the  angle  from  the  base 
line. 

To  lay  off  an  Odagon  in  a  Square. — Fig.  6.  Draw  the 
diagonals  e  and/!  Mark  ofF  the  distance  from  the  centre  g, 
on  all  the  sides,  measuring  from  the  corners.  The  resulting 
marks  give  the  corners  of  the  octagon. 

Fig.  7.  Another  method  is  to  measure  off  the  side  of  the 
square  on  its  diagonal  k.  Square  from  a  side  to  the  point 
thus  found  on  the  diagonal,  and  n  0  is  the  distance  to  be 
guaged  from  each  corner,  to  mark  the  corners  of  the  octagon. 


Fig.  6. 


Fig.  7, 


To  lay  off  an  Odagon  on  a  given  side. — Fig.  8.  Prolong  the 
^iven  side  a  b,  and  lay  off  an  angle  of  45°  at  both  a  and  b. 
The  lines  i,  2  are  squared  up  from  the  given  side,  also  lines 
3  and  4.  By  applying  the  square  to  the  other  lines  we  get 
the  remaining  sides. 

To  make  a  square  stick  odagonal. — Fig.  9.  Lay  the  square 
or  two-foot  rule  diagonally  across  the  stick  so  as  to  measure 
two  feet  on  it,  letting  the  corners  on  the  same  side  of  the  blade 
or  rule  touch  the  edges  of  the  stick.  Make  marks  at  the  7  in. 
and  the  17  in  marks.     Measure  thus  at  each  end  of  the  stick. 


22 


STEEL     SQUARES 


Lines  struck  through  these  points  show  what  is  to  come  off  to 
make  it  octagonal. 

To  find  the  side  of  an  Octagon  when  the  side  of  the  square  is 
given. — Multiply  the  side  of  the  square  by  5  and  divide  by  12 
The  quotient  is  the  side  of  the  inscribed  octagon. 


When  the  side  of  the  Octagon  is  given,  to  find  the  square  width. 
— Suppose  the  side  of  the  octagon  is  to  be  16  ft. ;  take  half  this 
or  96  in.  for  the  square,  16  in.  on  both  tongue  and  blade  taken 
6  times,  giving  11  ft. 3J  in.,  which,  being  doubled  and  added 
to  the  side  of  the  octagon,  gives  the  square  width. 


7^ 

% 

^<^ 

\~ 

A 

\ 

>^A 

^ 

V 

1^ 

\ 

^ 

~VL 

\ 

^ 

ik 

Fig.  9. 

Octagonal  and  Hexagonal  Roofs. — Fig.  10  represents  an 
octagonal  roof  In  its  construction  the  suggestions  on  octa- 
gons, herein  made,  must  be  referred  to.  The  length  of 
hips  is  found  as  usual  from  rise  and  run,  the  run  being  half 
the  diagonal  of  the  octagon.     Cut  the  first  pair  full  length 


AND     THEIR      USES. 


23 


to  butt  against  each  other ;  the  next  pair  are  to  be  set  up  at 
right  angles  to  these,  and  each  is  to  be  cut  shorter  than  the 
first  pair  by  half  the  thickness  of  first  pair,  measured  square 
back  from  the  down  bevel.  The  third  and  fourth  pairs  are 
to  be  cut  shorter  than  the  first  by  half  the  diagonal  of  a 
square  whose  side  is  the  thickness  of  the  first  rafters.  If  the 
thickness  of  the  first  pair  is  2  in.,  then  the  third  and  fourth 
pairs  are  shortened  by  i-^^,  as  2-J-0.  is  the  diagonal  of  a  square 
whose  side  is  2. 

The  first  and  second  pairs  have  no  side  bevels  ;  the  side 
bevels  of  the  third  and  fourth  run  back  on  both  sides  from 


Fig.  10. 

the  middle  of  the  rafter.  Find  this  bevel  by  taking  the 
original  length  of  rafter  on  the  blade  and  its  run  on  the 
tongue,  when  the  blade  shows  the  cut.  The  backing  of  the 
hips  obtain  by  taking  -^  of  the  rise  on  the  tongue  and  the 
length  of  hip  on  blade,  the  latter  giving  the  cut ;  for  the  side 
of  an  octagon  is  -^  its  square  width. 

Half  the  square  width  is  the  run  of  the  middle  jack-rafter, 
from  which  and  its  rise  we  get  its  length.  From  the  length 
deduct  the  same  amount  as  from  the  third  and  fourth  pairs  of 
hips.     If  there  are  to  be  two  jacks  between  the  middle  one 


24  STEEL      SQUARES 

and  the  corner,  we  divide  the  length  of  side  into  three  parts, 
also  the  rise,  whence  are  obtained  as  before  the  distance  ol 
rafters  apart,  and  the  rise  of  shortest  jack.  Divide  half  the 
square  width  of  octagon  by  three  to  find  the  run  of  shortest 
jack.  Just  as  the  square  is  laid  on  to  find  the  length  of  a  jack, 
it  gives  the  down  and  lower  end  bevels  ;  while  the  side  bevel 
is  obtained  by  taking  length  of  middle  jack  on  blade  and  half 
one  side  of  the  octagon  on  the  tongue  ;  the  blade  giving 
the  cut. 

A  Hexagonal  Roof. — The  side  of  a  hexagon  equals  the 
radius  of  the  circumscribing  circle.  The  square  width  is 
determined  from  two  parallel  sides ;  a  diagonal  of  the  figure, 
is  a  line  from  opposite  angles. 

The  first  pair  of  hips  are  set  up  as  in  the  octagonal  roof. 
The  second  and  third  pairs  have  a  side  bevel.  To  find  this, 
take  half  the  side  of  the  hexagon  on  the  tongue  and  half  the 
square  width  added  to  the  gain  of  the  hip-rafter  in  running 
that  distance,  on  the  blade.  The  tongue  gives  the  cut.  Strike 
the  bevel  across  the  rafter.  Now,  the  second  and  third  pairs 
are  to  be  measured  back  shorter  than  the  first  pair,  on  their 
middle  lines,  just  half  the  length  of  this  bevel.  The  third 
pair  has  the  bevel  cut  on  both  sides  from  the  centre.  The 
backing  of  the  hips  is  found  by  taking  y-j^^-  the  rise  of  roof  on 
the  tongue  and  the  length  of  hip  on  blade ;  the  latter  gives 
the  cut.  The  side  of  a  hexagon  is  -^-^  its  square  width,  or 
apothem.  The  lengths  and  bevels  of  the  jack-rafters  are  found 
as  in  octagonal  roofs. 

Hexagonal  and  Octagonal  Boxes  or  hoppers.  — The  cuts  for 
the  edges  of  the  pieces  of  a  hexagonal  hopper  are  found  by 
subtracting  the  width  of  one  piece  at  the  bottom,  viz.,  the 
width  of  same  at  top,  and  taking  the  remainder  on  the  tongue. 


AND      THEIR      USES. 


25 


and  depth  of  side  on  blade.  The  tongue  gives  the  cut.  For 
the  cut  on  the  face  of  the  sides,  take  -^  of  the  rise  on  the 
tongue,  and  the  depth  of  side  on  the  blade.  The  tongue 
gives  the  cut.  The  bevel  for  the  top  and  bottom  edges  is 
found  by  taking  the  rise  on  the  blade  and  the  run  on  the 
tongue.      The  latter  gives  the  cut. 

To  find  the  cut  of  an  octagonal  hopper  (Fig.  11)  for  the 
face  of  the  board  and  also  the  edge,  subtract  the  rise  from  the 
width  of  side  ;  take  the  remainder  on  the  tongue  and  width  of 


Fig.   11. 

side  on  blade ;  the  tongue  gives  the  cut.  The  edge  of  the 
stuff  is  to  be  square  when  applying  the  bevel.  The  bevel  for 
the  top  and  bottom  edges  of  the  sides  is  found  by  taking  the 
rise  on  the  blade  and  run  on  the  tongue,  the  latter  giving  the 
cut.  This  makes  the  edges  horizontal.  The  edges  are  not 
to  be  beveled  till  the  four  sides  are  cut. 

To  test  a  square  with  the  compasses,  draw  the  two  con- 
centric arcs,  d  and  c,  Fig.  12,  with  radii  of  6  and  8  in.  Set 
the  compasses  to  10  in.,  and  inserting  one  point  anywhere 
on  the  outer  arc,  as  c,  mark  the  exact  distance  on  the  inner 
arc,  as  at  d.  Connecting  these  points  with  the  centre  of  the 
two  arcs,  we  have  an  exact  right  angle  with  which  to  compare 


26  STEEL      SQUARES 

the  square.     To  test  a  framing  square,  it  is  best  to  draw  arcs 
of  12  and  1 6  in.  radius,  laying  off  20  in.  between  c  and  d. 

The  square  may  be  more  quickly  tested  by  laying  it  on  a 
wide  board,  placing  the  blade  parallel  to  one  edge,  which 
must  be  planed  perfectly  straight,  and  drawing  a  fine  line 
along  the  tongue.  The  square  is  then  turned  over,  so  as  to 
rest  in  a  reversed  position  on  the  opposite  side  of  the  line  just 
drawn.  If  the  square  now  exactly  coincides  with  the  line  and 
the  board-edge,  it  is  a  perfect  right  angle.  A  great  recom- 
mendation of  this  method  is  that  an  inaccuracy  of  the  scale  is 
doubled  by  the  reversing,  and  so  made  more  apparent.  If  the 
square  is  not  true,  it  should  be  set  in  a  vise  and  draw  filed. 


I! 


i^ 


Fig.  12.  Fig.  13. 

To  find  the  centre  of  a  Circle  with  the  Square.  — Fig.  1 3.  Lay 
the  square  on  the  circle  with  the  corner  at  the  circumference. 
Mark  where  outer  edge  of  tongue  and  blade  cut  the  circle, 
and  draw  a  line  connecting  these  points.  This  line  is  always 
a  diameter,  and  by  drawing  in  like  manner  a  diameter  in 
another  direction,  the  intersection  of  the  two  gives  the  centre. 

Three  points  not  in  a  straight  line  bei?ig  given,  to  find  the  centre 
of  a  circle  which  will  pass  through  them. — Fig.  \\.  Let  i,  2 
and  3  be  the  points.  Connect  them  by  straight  lines,  and 
square  from  half  the  distance  between  them  as  at  d  and  e. 
The  intersection  of  these  perpendiculars  is  the  centre. 

This  will  be  discussed  at  length  further  on. 


AND     THEIR     USES. 


27 


To  find  a  Circle  equal  in  area  to  two  or  more  Circles.  — Fig.  1 5. 
Let  A  be  f  in.  in  diameter,  and  B  ij  in.  Measure  across 
from  the  |  in.  on  one  arm  of  the  square  to  the  \\  in.  on  the 
other  ;  this  distance  is  the  diameter  of  the  required  circle,  C. 

5 


c-' 


Fig.  14. 

If  there  were  three  circles,  we  should  set  the  diameter  of  the 
third  on  the  tongue  and  that  of  C  on  the  blade ;  and  the 
diagonal  distance  between  these  points  would  be  the  diameter 
of  a  circle  equal  to  the  three,  and  so  on  for  any  number. 


Fig.  IS. 


This  applies  to  squares  also.  By  this  simple  rule  we  can  find 
the  size  of  one  pipe  equal  to  two  or  more,  and  square  spouts 
in  like  manner.  Similar  figures  of  all  kinds  may  be  worked 
by  this  method — triangles,  rectangles,  hexagons,  octagons, 
etc.,  taking  similar  dimensions  only;  that  is,  if  the  shortest 


28 


STEEL     SQUARES 


side  of  one  triangle  is  taken,  the  shortest  side  of  the  other 
must  be  taken  also,  and  the  answer  gives  the  shortest  side  of 
the  required  triangle. 


To  find  the  side  of  a  square  of  half  the  area  of  a  given  square. 
— Fig.  1 6.  Let  G  be  the  given  square;  half  its  diagonal 
gives  the  side  of  the  smaller  square.  A  square  constructed  on 
the  diagonal  of  G  would  contain  double  the  area. 


Fig.  i6. 

Equilateral   Triangle. — An    equilateral    triangle    may   be 


AND      THEIR      USES. 


29 


obtained  by  the  use  of  the  square,  if  the  length  of  one  side 
is  given  :  suppose  B  C,  Fig.  16,  the  length  of  one  side,  then 
take    10  inches  on  the  blade  and   17  inches  on  the  tongue  of 


Fig.  17. 

*he  square  and  apply  on  a  line,  as  at  B  C,  resting  the  10  inch 
mark  at  the  point  B.  Draw  a  line  from  B  to  A.  Reverse 
the  square  and  place  10  inches  at  the  point  C,  then  on  the 


Fig.  18. 

tongue  keep  the  17  inch  mark  on  the  line  B  C,  and  draw 
the  line  C  A  until  it  cuts  the  line  B  A ;  then  will  B  A  be 
equal  to  the  line  A  C,  which  is  equal  to  the  line  B  C. 


30 


STEEL   SQUARES 


Of  course  this  figure,  when  within  the  range  of  a  pair 
of  compasses,  may  be  constructed  very  simply,  as  follows : 
Take  the  length  of  one  side  of  the  triangle  on  compass,  place 
one  foot  on  C,  describe  an  arc  at  A  ;  then  with  one  foot  of 
the  compass  at  B  describe  the  arc  A,  and  the  three  points  of 
the  figure  are  given  ;  join  A  B,  B  C,  and  A  C  ;  the  figure 
will  then  be  complete. 


Method  of  Dividing  Angles.— K  B  C,  Fig.  17,  is  an  acute 
angle.  We  wish  to  divide  it.  Measure  up  from  B  to  A 
any  distance,  make  B  C  the  same  distance,  place  the  square 
on  the  points  A  and  C  as  shown,  keeping  the  distance  on  the 
blade  and  tongue  the  same,  then  the  heel  or  corner  of  the 
square,  S,  will  give  the  points  through  which  to  draw  a  line 


AND      THEIR      USES. 


31 


passing  through  the  angle  at  B,  and  the  division  will  be  com- 
plete. 

Again  :   Let  Fig.  18  be  an  obtuse  angle  ;  make  B  A  and  B 


C  equal.     Apply  square  as  shown,  keeping  equal  distances  on 
blade  and  tongue  at  the  points  of  contact  A  and  C. 

The  point   E  on  the  heel  of  sc^uare  will  be  one  point 


32 


STEEL      SQUARES 


from  which  to  draw  a  line  through  B,  which  forms  the  division 
of  the  angle. 

At  Fig.  19  I  show  a  number  of  angles,  which  are  treated 
same  as  foregoing.  At  the  junction  of  the  lines  drawn  from 
the  angles  B  B  B,  the  centre  of  the  triangle  is  found  at  P. 

B 


Fig.  21. 

This  method  of  bisecting  an  angle  is  very  useful,  inasmuch 
as  the  ''cut "  or  mitre  of  any  mouldings  placed  at  any  angle 
on  a  flat  surface  may  be  obtained.  This  is  shown  at  Fig.  20, 
which  may  be  a  panel  or  other  like  surface.     This  diagram 


Fig.  22. 

shows  that  angles  of  any  form  and  in  any  position  may  be 
equally  divided  by  a  proper  use  of  the  steel  square. 

Suppose  we  want  to  find  the  angle  45°  on  a  board,  we 
mark  any  two  points  A  C,  Fig.  21,  on  the  edge  of  a  board  ; 


AND     THEIR     USES. 


33 


apply  the  square  as  shown,  keeping  its  sides  on  A  C  ;  then 
the  distance  on  each  side  of  the  square  being  equal,  measuring 


Fig.  23. 


from  its  heel  or  corner  B  gives  the  angle  45°.     H  this  portion 
be  cut  out  it  will  form  a  templet  or  set  square  which  is  very 


Fig.  24. 

useful  in  drawing.     The  lines  A  B  and  C  B  are  true  mitres, 
or  angles  of  45*,  with  the  line  A  C  as  their  base. 


34 


STEEL  SQUARES 


A,  B,  C,  R  at  Fig.  22  show  the  lines  for  forming  a  set-square 
having  60°  on  the  line  A  R,  and  30°  on  C  R.  This  figure  is 
formed  with  compasses,  as  follows  ;  Make  A  C  length  of  base 


line  ;  let  B  be  half  the  distance  between  A  C.  From  C  B  as 
centres  and  radius  make  the  intersection  at  R,  then  by  joining 
A  R  and  C  R  the  angles  30°  and  60°  are  formed.    This  is  the 


AND     THEIR     USES.  35 

principle.  To  do  all  this  with  the  square,  simply  take  the 
length  of  the  square — 24  inches — on  the  blade  and  thirteen 
inches  on  the  tongue,  and  place  these  points  on  the  line  ABC, 
Fig.  23,  and  you  have  the  angles  at  once.  If  the  figure 
required  is  greater  than  the  square  can  cover,  then  continue 
the  line  A  D  to  the  length  required ;  then  square  down  until 
the  line  cuts  ABC,  and  the  work  is  done.  If  a  smaller  figure 
is  wanted,  measure  off  on  A  D,  or  A  B  C,  and  square  over. 

At  Fig.  24  I  show  a  quarter  of  a  circle  trisected  or  formed 
into  angles  of  30,  60  and  90  degrees  ;  12  and  7  by  the  square 
will  give  30°  and  12  and  21  will  give  the  angle  of  60°.  These 
are  things  to  remember,  as  the  carpenter  and  joiner  will  find 
them  very  useful  in  his  everyday  work. 

To  find  a  Tangent. — To  find  a  Tangent  to  the  arc  of  a 
circle,  divide  the  chord  A  C  (Fig.  25)  in  B  ;  from  B  square  up 
a  line  cutting  in  K,  giving  it  as  a  point,  through  which  draw 
square  with  K  A  as  shown  cutting  in  R,  making  K  S  equal 
K  R  ;  draw  from  S  through  A,  and  the  line  is  tangent  to  the 
arc  at  point  A. 

The  steel  square  may  be  used  as  shown,  to  good  advantage. 

This  problem  is  very  useful  to  stair-builders  and  other 
practical  workmen  operating  on  circular  work,  where  tangents 
must  be  found  to  make  proper  lines  for  joints.  To  find  a 
point  that  will  be  the  centre  of  a  circle  touching  any  three 
points  not  in  a  straight  line  :  Let  ABC,  Fig.  26,  be  three 
points  through  which  4t  is  desired  to  describe  a  circle  or  seg- 
ment of  a  circle  ;  connect  B  C,  also  B  A  ;  divide  A  B  at  i  ; 
then  square  down  at  i  with  the  steel  square,  and  continue  the 
line  indefinitely.  Divide  B  C  also  equally  at  2,  then  square 
down  at  this  point  as  shown ;  continue  the  line  until  it  crosses 
the  line  starting  from  i  B  A.     At  the  junction  of  these  lines 


36  STEEL      SQUARES 

set  one  leg  of  the  compass  and  extend  the  other  to  either  of 


the  points  ABC;  describe  a  circle,  and  it  will  be  found  that 


AND      THEIR     USES. 


37 


its  circumference  will  touch  the  points  ABC  exactly.     The 
same  problem  is  shown  at  Fig.  27,  where  the  lines  starting 


from  I  and  2  are  continued  to  S,  which  is  the  centre  of  the 
circle  whose  circumference  touches  the  points  ABC. 


38 


STEEL     SQUARES 


This  method  of  finding  a  centre  of  any  segment,  such  as 
part  of  a  circle,  is  one  of  the  most  useful  known  in  the  art  of 
constructive  carpentry,  as  it  enables  the  workman  to  get  the 
exact  sweep  of  any  circle,  arch,  window  or  door-head,  if  he  has 
but  the  width  of  the  opening  and  the  rise  or  height  of  the  arch 
given  him. 

As  an  illustration,  I  show  at  Fig.  28  a  portion  of  a  door- 
way with  a  segmental  head.  Suppose  the  doorway  to  be  three 
feet  and  six  inches  wide,  and  the  rise  to  be  nine  inches  only. 
Now  set  off  the  width  as  shown,  then  the  height  from  the  spring 


line  A  C  at  equal  distances  from  each  point,  connect  A  B  and 
B  C,  proceed  as  in  the  other  problems,  and  the  centre  of  the 
circle  will  be  found  at  S. 

In  many  cases  it  will  be  impossible  to  use  compasses  or 
even  an  ordinary  trammel,  for  in  large  openings  or  arches  for 
bridges  or  other  work  the  trammel  could  not  be  used.  When 
such  is  the  case  a  tape  line,  or  sometimes  a  strong  cord  may 
be  used,  or  even  a  surveyor's  chain.  In  making  centres  for 
bridge  work  or  for  large  openings  in  buildings,  the  angles  of 
the  voussoirs  and  key  stones  may  be  obtained  and  laid  off  on 
the  sides   of  the   centres,  or   they  may  be  marked  off  and 


AKD     THEIR     USIS. 


39 


measured  and  placed  on  paper  or  on  the  drawing  board  until 

required. 

This  problem  may  be  applied  to  many  cases  m  carpen- 
ter's work,  sheet  metal  work,  and  in  laying  out  curves  of  any 
sort ;  and  I  would  advise  the  young  mechanic  to  learn  it 
thoroughly  and  apply  it  as  often  as  possible. 

It  frequently  happens  that  the  skilful  carpenter  or  joiner 
is  called  upon  to  perform  some  work  which  justly  belongs  to 
the  architect,  but  which  in  many  instances  the  architect  him- 
self does  not  know  how  to  practically  operate.     For  instance  : 


Fig.  29. 

It  is  a  well  known  fact,  that  if  a  column  is  formed  with  a 
straight  line  down  its  side  in  the  direction  of  its  length,  when 
completed  it  will  appear  as  though  it  was  made  concave,  or 
of  less  relative  diameter  half  way  down,  than  it  really  is.  This 
peculiarity  was  well  known  to  the  Egyptians  and  provided 
for,  but  it  remained  for  the  Greeks  to  discover  the  ''why  and 
wherefore  "  and  apply  a  scientific  remedy.  Of  course,  many 
columns  are  now  made  with  straight  tapering  sides,  or 
parallel  from  base  to  neck,  but  this  is  not  the  best  or  most 
scientific  manner,  and  I  now  propose  to  show  how  a  line 


40  STEEL  SQUARES 

may  be  obtained  by  the  use  of  the  square  and  a  rod,  that  will 
be  conoidal,  which  is  the  name  given  to  a  curve  described  as 
I  am  about  to  show. 

Take  the  square  and  place  as  shown  at  A  and  B,  Fig  29. 
Draw  a  line,  G,  which  must  be  straight  with  the  lower  edge 
of  the  blade  B.  Then  measure  the  height  of  the  column  on 
the  outside  edge  of  the  blade,  A — in  scale,  of  course — and  draw 
the  line  I  at  right  angles  to  A.  On  the  line,  G,  measure  a 
distance  equal  to  half  of  the  diameter  of  the  base,  and  on 
line  I  measure  a  distance  equal  to  half  the  diameter  of  the 
top  of  column.  Then  take  a  rod,  C,  and  make  a  hole  in 
one  end,  to  hold  a  pencil,  D  ;  from  the  centre  at  D  measure 
a  distance  equal  to  half  the  diameter  at  base,  and  drive  in  a 
nail,  E.  Now  bring  the  pencil,  D,  to  I  and  make  the  nail,  E, 
touch  the  edge  of  the  blade,  A.     This  done,  drive   in  a  nail, 

F,  so  that  it  will  just  touch  the  edge  of  the  blade,  B,  or  the  line 

G.  All  is  now  ready  :  move  the  pencil,  D,  to  G,  being  care- 
ful to  see  that  the  nails  slide  along  smoothly  on  the  edges 
of  the  square,  and  the  pencil,  D,  will  describe  the  curve 
desired. 

In  case  a  full-sized  templet  or  curve  is  required,  all  that 
has  to  be  done  is  simply  to  nail  down  on  a  clean  floor  two 
strips  of  wood  in  imitation  of  a  large  square,  making  sure  the 
strips  are  long  enough  to  make  the  curve  as  long  as  the 
column  required.     The  rest  is  quite  easy. 

A  templet  of  this  kind  can  be  reversed  and  made  con- 
cave, so  as  to  try  on  the  work  as  it  progresses.  Sometimes 
the  curve  obtained  by  this  method  is  designated  as  "the 
curve  of  diminution."  Among  architects,  however,  the 
curve,  or  rather  the  swelling  of  a  column  or  pillar  or  newel 
post,  in  the  centre  is  known  as  Entasis. 

There  are  many  other  ways  of  getting  this  curve,  but  I 


AND     THEIR     USES. 


41 


do  not  know  of  any  that  is  better  than  the  one  shown,  or  so 
easily  understood  by  the  operative  workman. 

The  Diagonal  Scale. — In  the  first  volume  of  The  Steel 
Square  and  its  Uses,  I  gave  a  brief  account  of  the  diagonal 
scale  as  shown  on  the  No.  lOO  square.  I  propose  here  to 
dwell  at  length  on  this  department  of  the  tool,  and  show 
to  what  extent  this  scale  may  be  employed. 

On  Fig.  30  I  show  a  diagram  of  the  scale  enlarged  and 


Fig.  30. 


lettered  for  this  occasion  ;  and  I  may  here  state  that  the 
workman  will  find  no  difficulty  in  adapting  the  diagrams  and 
what  follows  to  the  scale  as  depicted  on  his  own  square. 

From  the  numerous  inquiries  I  have  had  I  am  led  to 
believe  that  the  diagonal  scale  is  not  so  well  understood  or 
appreciated  as  it  ought  to  be,  which  is  certainly  to  be  regretted. 
This  scale  is  intended  for  minute  measurements,  and  when 
a  thorough  knowledge  of  its  properties  are  understood,  it  is 
not  a  very  difficult  operation  to  so  employ  it  that  the  500th 
part  of  an  inch  may  be  obtained,  and  for  the  practical  work- 
man this  is,  perhaps,  minute  enough,  though  to  the  advanced 
scientist  this  would  be  considered  a  trifling  operation,  when 
such  minute  measurements  are  used  as  the  5000th  part  of 
an  inch. 


42 


STEEL     SQUARES 


In  actual  practice  the  scale  is  never  used  to  find  the 
smaller  measurements,  but,  it  may  sometimes  happen  that 
the  workman  may  want  to  measure  a  plan  or  take  a  distance 
on  a  map  pretty  accurately,  then  a  fine  subdivision  will  be 
found  useful. 

In  order  to  give  the  reader  a  fair  understanding  of  the 
principles  on   which   this   scale   is   founded,    I   illustrate  its 
construction  and  the  manner  in  which  it  is  used, 
and  in  doing  so  I  will,  for  convenience  sake,  quote 
from  an  excellent  authority  on  the  subject : 
HH  ' '  Let  us  draw  a  diagram,  Fig.  3 1,  say  three  times 

the  size  of  the  first  division  of  the  scale  as  shown 
on  the  square.  Imagine  the  short  distance  from 
A  to  B  to  represent  ten  inches ;  it  will  be  evident 
to  any  one  that  to  divide  that  short  space  into 
ten  equal  parts  would  simply  confuse  the  whole 
diagram  ;  but  if  we  adopt  another  plan  and  divide 
it  into  ten  parts  on  its  length,  as  shown,  and 
then  draw  a  diagonal  line  from  B  to  C,  we 
have  the  distance  A  B  divided  into  ten  parts. 

The  numbers  shown  in  the  diagram  indicate 
the  fractional  parts  of  the  line  A  B,  and  if  we  take 
our  compasses  and  place  one  leg  on  the  line  A  C, 
at  number  five,  and  the  other  leg  where  the  diag- 
onal line  cuts  the  line  five  ;  that  distance  will  be  found  to  be 
just  one-half  of  the  distance  between  A  and  B.  There  is  a 
difference  of  one-tenth  of  the  whole  distance  between  A  B, 
at  every  point  where  the  diagonal  cuts  the  cross  lines.  Or  in 
other  words,  where  the  diagonal  crosses  the  horizontal  lines, 
the  point  of  juncture  is  one  inch  nearer  to  the  line  A  C, 
than  the  next  point  lower  down." 

This  is  the  principle  on  which  the  diagonal  scale  is  based, 


Fig.  31 


ANDTHEIRUSES.  43 

and  it  will  be  seen  that  any  fraction  of  a  foot  or  an  inch  may 
be  so  divided  by  diagonals  that  the  most  minute  subdivisions 
may  be  obtained. 

The  measurements,  of  course,  are  always  taken  along 
the  horizontal  lines,  and  measured  from  the  perpendicular 
to  the  diagonal. 

With  a  thorough  knowledge  of  the  foregoing  it  will  be 
easy  to  understand  that  the  perpendicular  is  not  necessarily 
limited.  It  may  be  made  twice  or  four  times  the  length, 
and  divided  into  twice  or  four  times  the  number  of  parts 
which  would  render  the  diagram  to  make  reading  of  200ths 
and  400ths  respectively. 

If  twelfths  of  an  inch  or  foot  are  wanted,  all  that  is 
required  is  to  divide  the  height  into  twelve  parts  instead  of 
ten,  draw  the  diagonal,  and  the  twelfths  are  there. 

In  using  this  scale  let  us  examine  it  at  Fig.  ^o,  and  we 
will  see  that  the  other  divisions  are  in  inches,  so  to  apply 
the  rule  we  proceed  as  follows  :  For  instance,  we  want  one 
inch  and  forty-six  one-hundredths,  place  one  leg  of  the  com- 
pass on  the  one  inch  mark  and  the  other  leg  where  the  diag- 
onal cuts  the  line  at  4,  on  the  sixth  division  up.  This  gives 
the  length  required. 

The  foregoing  description  and  explanation  applies  to  the 
diagonal  scale  that  generally  accompanies  a  case  of  drawing 
instruments,  as  well  as  to  the  scale  on  a  steel  square. 

It  may  be  well  to  state  here  that  some  new  squares  recently 
placed  in  the  market,  and  known  to  the  trade  as  No.  200, 
have,  in  place  of  the  diagonal,  a  graduated  line  or  scale, 
with  the  subdivisions  of  the  inch  marked  off  in  looths.  This 
innovation  is  said  by  the  manufacturer  to  be  "an  improve- 
ment." If  it  is,  the  "improvement,"  in  my  opinion,  is  a 
questionable  ©ne. 


44 


STEEL  SQUARES 


To  Make  Flared  Circular  Work. — This  problem  will  some- 
times be  found  useful  to  the  wood-worker,  but  it  is  more  par- 
ticularly adapted  for  the  use  of  tin  and  sheet-metal  workers  - 


.^ 


Fig.  32. 


Place  the  square  as  shown  at  Fig.  32,  A,  B,  i  and  17.  Do 
not  alter  the  position  of  the  square,  but  lay  off  one-half  the 
large  diameter  of  the  work  in  hand,  at  A  B.     Then  measure 


Fig.  33. 

from  A  to  I  the  depth  of  the  work  ;  now  move  the  square 
down  to  I  as  shown  and  draw  a  line  ;  on  this  line  mark  off 
the  distance  of  half  the  small  diameter  of  work,  as  at  i,  8; 


AND      THEIR      USES.  45 

draw  line  from  B  to  8  until  it  crosses  line  at  17;  now  set 
compasses  at  17  and  8,  and  describe  circle  at  h,  Fig.  33  ; 
then  set  compass  at  17  and  B  and  draw  circle  z',  Fig.  -i^i) 
draw  the  line/,  Fig.  'i^'},  ;  divide  the  circumference  into  any 
number  of  pieces — I  show  these  in  this  case — and  take  a  piece 
of  cardboard  or  other  flexible  material,  and  measure  off  on  the 
line  h  the  number  of  divisions.  Draw  radial  lines  to  centre 
as  shown.  Allow  extra  material  for  joining.  Any  flaripg 
piece  of  work  on  a  circular  plan  can  be  made  by  this  method. 

Steel  Squares  Generally. — The  Frontispiece  exhibits  three 
different  styles  of  steel  squares — the  bridge-builder's  square, 
the  machinist's  square  and  the  carpenter's  square.  The  pecu- 
liarity of  the  bridge-builder's  square  is  that  the  blade  is  three 
inches  wide,  having  a  slot  twenty-one  inches  long  and  one 
inch  wide  down  its  centre.  It  will  be  easy  to  see  how  useful 
this  square  is,  as  it  may  be  used  for  2  in.  or  3  in.  mortises 
with  either  2  or  3  in.  shoulders,  or,  when  occasion  requires, 
it  may  be  used  for  one  inch  mortises  or  one  inch  tenons. 
One  and  a  half  inch  mortises  and  tenons  may  be  laid  out  with 
the  blade  of  the  square.  This  square  also  has  other  useful 
features  which  will  readily  be  seen  by  the  practical  workman. 
Nearly  all  of  the  problems  shown  in  this  volume  may  be  solved 
by  this  square,  but  it  does  not  possess  for  the  regular  workman 
that  usefulness  which  is  attributed  to  the  carpenter's  square. 

The  small  square  shown  is  made  specially  for  machinists, 
and  is  very  handy  for  men  who  have  charge  of  wood-working 
machinery.  It  is  also  very  useful  as  a  bench  square,  and 
should  find  its  way  into  every  carpenter's  and  joiner's  kit. 

The  No.  100  square  shown  is  the  carpenter's  square,  and 
is  the  one  by  which  all  the  problems  shown  in  this  work  have 
been  solved.  An  exhaustive  description  of  all  the  figuring  on 
this  square  may  be  found  in  my  first  treatise  on  The  Steel 


46  STEEL      SQUARES 

Square  and  its  Uses,  a  copy  of  which  the  reader  of  this  should 
obtain,  if  he  has  not  already  secured  one. 

There  is  a  square  made,  the  blade  of  which  is  1.7  in.  wide 
and  twelve  inches  long ;  the  tongue  is  nine  inches  long  and 
one  inch  wide.  It  is  figured  in  inches,  half  inches,  quarters, 
eighths  and  sixteenths.  It  is  a  very  handy  square,  and  often 
useful  where  either  a  larger  or  smaller  one  would  be  of  no 
service. 

Besides  the  squares  mentioned  in  the  foregoing  there  are 
several  others,  such  as  the  stonecutter's  square,  which  has  a 
blade  thirty  inches  long  and  two  inches  wide,  and  a  tongue 
two  feet  long  and  one  and  a  half  inches  wide.  The  blade  and 
tongue  are  marked  into  one-eighths,  quarters,  half  inches  and 
inches.  They  are  excellent  tools  for  stonecutters,  some  of 
whom  are  quite  expert  in  their  use.  The  price  of  these  squares 
is  about  three  dollars  and  fifty  cents. 

There  is  also  a  square  made  called  *  *  The  Flat  Steel  Square, " 
which  is  often  found  useful  for  some  sorts  of  work.  It  is 
similar  to  the  ordinary  carpenter's  square,  but  is  not  tapered 
in  its  thickness,  nor  is  it  figured  the  same,  showing  only 
eighths,  quarters,  halves  and  inches. 

There  is  also  an  iron  square  made  which  sells  for  about 
$1.50,  and  which  is  generally  used  by  blacksmiths,  brick- 
layers and  some  wagon  makers.  Why  these  mechanics  should 
use  such  inferior  tools  as  this  is,  I  cannot  understand,  unless  it 
is  on  the  scale  of  economy,  which  in  this  case  is  certainly 
misapplied. 

A  new  square,  called  "  The  Crenelated  Steel  Square,"  has 
lately  come  into  use,  which  has  little  notches  cut  along  the 
inside  edge  of  the  tongue.  I  give  herewith  an  illustration  of 
it.  Fig.  34,  and  quote  from  the  inventor's  circular  the  object 
of  the  invention  : 


AND      THEIR      USES. 


47 


*'  This  SQUARE  is  invaluable  to  the  mechanic.  It  is  designed 
to  facilitate  the  operation  of  marking  timber  for  mortises  or 
the  'Maying  off  a  frame."  At  the  same  time  it  secures  the 
utmost  accuracy.     It  excels  all  other  squares  for  carpenters' 


Fig.  34- 
THE    CRENELATED    STEEL   SQUARE. 

or  builders'  use.  Turning  the  timber  is  nearly  dispensed  with, 
as  three  sides  can  be  marked  while  it  remains  in  the  same 
position, 


4§  STEEL     SQUARES 

"By  the  use  oi this  square  one  man  can  lay  off  more  timber 
in  the  same  length  of  time  than  two  men  can  in  the  ordinary 
way. 

''You  can  mark  on  either  side  or  overhead." 

Directions  /or  Use.  — Take  the  square  in  the  left  hand,  lay 
the  tongue  of  the  square  upon  the  surface  to  be  marked,  for  a 
tenon  or  mortise,  lower  the  end  of  the  main  arm  of  the  square 
next  to  you,  say  about  two  or  three  inches  from  the  upper 
surface,  place  the  awl,  held  in  the  right  hand,  in  the  notch 
designating  the  distance  you  wish  to  have  the  mortise  or  tenon 
from  the  outer  surface,  gently  press  the  square  against  the 
timber,  and  with  one  toward  movement  the  mark  is  made. 

Replace  the  square  as  before,  place  the  awl  in  the  notch 
desired,  for  width  of  mortise  or  tenon,  and  again  mark  as 
before. 

For  a  mortise,  replace  again,  place  the  awl  in  a  notch 
equidistant  from  marks  already  made,  and  again  mark,  for 
guide  to  the  augur,  doing  away  with  witness  marks. 

In  using  a  pencil,  after  having  marked,  move  the  square 
back  a  trifle  before  moving  the  right  hand,  to  avoid  breaking 
the  pencil. 

The  same  rules  apply  to  its  use  in  marking  on  the  sides 
of  timber  or  overhead,  and  the  square  in  either  hand. 

I  may  also  add  that  the  square  is  so  figured  that  almost 
every  problem  shown  in  either  of  the  works  on  the  steel  square 
can  be  solved  with  it  if  skilfully  handled. 

As  this  work  is  intended  to  discuss  the  Steel  Square  and 
ITS  Uses  only,  I  do  not  feel  called  upon  to  say  anything  about 
other  kinds  of  squares,  of  which  there  are  many,  all  useful 
for  the  purposes  for  which  they  were  designed. 

I  show  at  Fig.  35  a  combination  tool  in  which  the  square 
is  the  most  prominent  feature.    The  intelligent  workman  will 


AND     THEIR     USES.  49 

have  no  difficulty  in  adapting  the  tool  to  a  great  variety  of 
work,  and  while  it  is  somewhat  cumbersome  and  scarcely 
adapted  for  the  everyday  uses  of  the  carpenter,  many  foremen 
and  master  builders  may  find  it  of  great  service.  The  device, 
I  believe,  was  patented  some  years  ago,  by  Mr.  P.  O.  King, 
of  Valley  City,  Dakota. 


Fig.  35. 

By  a  proper  adjustment  of  the  various  parts  of  this  com- 
bination tool,  angles  and  lengths  of  all  sorts  of  braces  and 
struts  may  be  obtained. 

The  steel  square,  A  (Fig.  35),  is  formed  with  longitudinal 
dovetail  grooves  in  the  faces  of  its  arms  to  receive  sliding 
screws.     The  36  in.  rule,  B,  has  a  longitudinal  slot  through  its 


t 


Fig.  38. 

face  for  the  sliding  screws  to  work  in  ;  this  slot  extends  to 
within  2  in.  of  one  end  and  within  5  in.  of  the  other  end. 
One  side  of  the  rule  is  divided  into  inches  and  twelfths,  and 
the  other  side  has  lumber  measurements  indicating  12,  14, 
16,  and  1 8  ft.,  or  other  lengths.  The  sliding  screws  (Fig.  38) 
are  so  constructed  as  to  form  scribers.     A  T-square  (Fig.  36) 


50 


STEEL     SQUARES 


may  be  formed  by  sliding  the  head-piece,  D,  on  one  end  of 
the  rule  ;  the  square  may  also  be  used  as  a  gauge  by  fitting 
the  rule  with  the  grooved   sliding  metal  block    S,  Fig.  39. 


Fig.    36. 

When  the  square  and  rule  are  combined,  as  shown  in  Fig.  35, 
the  tool  may  be  used  for  giving  the  angle  and  length  of  differ- 
ent  kinds  of  rafters    and  braces.     The    rule  can  be   readily 


Fig.  39' 

taken  off  and  put  on,  and  when  once  set  will  be  held  firmly 
by  the  set  screws.  When  the  tool  is  to  be  used  for  levelling, 
as  in  Fig.  40,  the  supports  F,  which  screw  into  the  rule  or 


Fig.  40. 

pass  around  it,  may  or  may  not  be  used.  The  method  of 
using  the  tool  as  a  level  is  clearly  shown  in  the  drawing  ; 
when  used  as  a  plumb  (Fig.  37),  the  string  is  placed  in  th^ 


AND      THEIR      USES. 


51 


slit  E,  as  in  Fig.  41.  The  yard  rule  may  also  be  used  as  a 
plumb  by  attaching  the  string  as  shown  in  Fig.  41.  Fig.  39 
shows  the  tool  arranged  to  be  used  also  as  a  beam  compass. 

If  this  instrument  is  in  the  market,  I  can  not  find  it.  I 
have  made  inquiries  at  many  of  the  large  dealers  in  such 
kind  of  tools,  but  up  to  writing  I  have  been  unable  to  find 
this  one. 

The  description  as  given  in  the  foregoing  is  taken  from 
the  inventor's  circular,  and  may  be  relied  upon,  as  I  have 
examined  the  tool  closely — on  paper — and  find  its  capabili- 
ties far  beyond  those  the  inventor  claims. 


Fig.  37. 


c- 

Fig.  4i 


Useful  Applicatio7is  of  the  Square. — At  Fig.  42  I  show  a 
very  useful  quality  of  the  square  or  right  angle,  when  used  in 
combination  with  the  quadrant,  and  equilateral  triangle. 

One  property  of  the  circle  is  that  its  radius  will  divide  its 
circumference  into  approximately  six  parts.  This  fact  gives 
us  the  idea  that  a  scale  may  be  so  constructed  that  it  will 


52 


STEEL      SQUARES 


divide    a   circle  into   any  number  of  parts  we   may   desire. 
The  construction  is  as  follows  : 

Through  E  draw  a  tangent  line  at  right  angles  with  B  E  ; 
on  the  radius  A  B  form  the  equilateral  triangle  intersecting  in 


Fig.     42. 

C-^then  A  C  divides  the  circumference  of  this  circle  into  six 
parts  ;  produce  the  lines  from  A  B  to  cut  the  tangent  in  D 
and  J— make  J  N  equal  E  D.  This  gives  E  N  for  one  of 
the  divisions  on  the  tangent  line  ;  the  others  being  equal  to 


AND      THEIR      USES.  53 

E  N,  forms  a  scale  by  which  the  circumference  of  the  circle 
may  be  divided  into  as  many  parts  as  may  be  desired  from 
one  to  twenty. 

For  example,  let  seven  be  the  number  required.  Draw 
the  line  A  N;  this  cuts  the  perpendicular  in  P,  giving  B  P  as 
the  length  of  a  chord  that  will  divide  the  circumference  into 
seven  equal  parts.  Suppose  the  radius  A  B  to  measure  by  a 
J  inch  scale,  nine  feet  one  inch,  and  the  length  of  the  chord 
B  P,  by  the  same  scale,  7  ft.  11  in.,  which  would  be  the 
length,  it  will  be  seen  the  method  produces  results  correct 
enough  for  all  practical  purposes. 

If  we  wish  to  divide  the  circumference  of  a  circle  into 
eight  parts  proceed  as  follows  :  Draw  from  A  to  the  point 
below  8  in  the  figure,  which  gives  B  R  as  the  length  of  chord 
for  eight  divisions. 

For  nine  divisions  :  Draw  from  A  to  the  point  below  10  ; 
this  gives  us  B  T  as  the  length  of  the  chord. 

Ten  divisions  may  be  made  by  drawing  from  A  to  the 
point  below  lo ;  this  gives  B  T,  which  is  the  length  of  chord 
required. 

For  eleven  divisions,  draw  from  A  to  the  point  below  1 1  ; 
this  gives  B  H  the  proper  length  of  chord. 

For  twenty  divisions  draw  from  A  to  the  point  below  20, 
which  gives  B  S  as  the  length  of  chord  for  twenty  parts. 

This  useful  and  elegant  construction  was  first  introduced 
by  the  celebrated  Peter  Nicholson  nearly  100  years  ago  and 
was  elaborated  and  improved  by  the  late  Robert  Riddell,  of 
Philadelphia,  of  whom  I  have  many  pleasant  remembrances. 

The  following  figure,  which  is  based  on  the  principles  con- 
tained in  the  foregoing,  has  been  known  to  advanced  work- 
men for  many  years,  and  although  it  has  appeared  in  several 
publications  during  the  last  twenty  years,  is  not  so  well  known 
among  workman  as  its  merit  for  usefulness  deserves 


54 


STEEL      SQUARES 


Suppose  the  lines  A  J  and  A  8  (Fig.  43),  to  be  the  blade 
and  tongue  of  the  square  shown  in  Fig.  44,  then  construct 
along  the  blade  divisions  as  shown  atJHFEDCBA. 
This  is  merely  an  example,  and  any  divisions  desired  may  be 
used  if  the  proper  bevels  are  used. 

Now  take  the  distance  from  A  to  J,  on  your  compasses, 
and  describe  a  large  circle,  with  A  (Fig.  44),  as  a  centre. 
With  H  A  as  radius,  describe  a  second  circle.  With  F  A 
describe  a  third  circle.     With  E  A,  as  a  radius,  describe  a 


Fig.  43. 

fourth  circle,  D  A  is  the  radius  for  the  fifth  circle,  and  C  A 
for  the  sixth,  and  B  A  gives  the  radius  of  the  mner  circle. 

This  figure  (44)  is  only  half-size,  being  J  inch  scale,  while 
Fig.  43  for  convenience  sake  is  made  on  a  scale  of  J  inch  ; 
so  the  operator  must  bear  this  in  mind  when  working  this 
problem. 

By  keeping  this  fact  m  view  the  following  solutions  may 
be  easily  rendered. 

The  large  circle  having  the  radius  A  J,  its  circumference 
is  required  to  be  divided  into  ten  equal  parts ;  these  are  found 
by  setting  a  bevel  to  5^  inches  on  the  blade  of  the  square,  and 
3f  inches  on  the  tongue.  The  bevel  as  now  set  must  be 
applied  to  J  (Fig.  43),  and  a  straight  edge  placed  against  the 


AND     THEIR     USES. 


55 


blade  of  bevel,  it  will  show  a  straight  line  cutting  the  tongue 
of  blade  at  7,  giving  P  7  for  length  of  chord  required  which 
stepped  around  the  larger  circle  will  divide  it  into  ten  equal 
parts. 


Fig.  44. 


The  next  circle  having  the  radius  A  H,  is  to  be  divided 
into  nine  equal  parts.  Proceed  as  before  by  setting  bevel  on 
5^  inches  on  blade,  and  3^  inches  on  tongue.    Now  apply  at  H 


56  STEEL     SQUARES 

(Fig.  43),  run  line  on  blade  of  bevel  to  point  6,  giving  P  6 
for  length  of  chord  wanted. 

Now  take  third  circle  A  F,  the  circumference  of  which  we 
will  divide  into  seven  parts.  Set  the  bevel  to  5  J  inches  on  blade 
and  4f  inches  on  the  tongue.  Apply  at  F  (Fig.  43),  apply- 
straight  edge  as  before,  and  it  will  give  you  the  point  8,  then 
P  8  will  be  the  length  of  chord  sought,  and  will  divide  the 
circle  into  seven  equal  parts. 

The  next  circle,  with  A  E  for  radius,  is  required  to  be 
divided  into  nine  parts  ;  we  set  our  bevel  at  5  J  on  the  blade 
of  square,  and  at  3^  on  the  tongue.  Apply  at  E  (Fig.  43), 
use  straight  edge  as  before  which  will  give  you  point  5  ;  thus 
P  5  is  the  length  of  chord  required,  and  will  divide  the  cir- 
cumference into  nine  equal  parts. 

It  will  be  seen  that  the  bevel  is  at  the  same  angle  for  A  E, 
as  it  was  for  A  H,  and  that  each  of  these  circles  are  divided 
into  nine  equal  parts,  though  the  diameters  are  unequal, 
hence  it  will  be  seen  that  the  same  angles  divide  any  sized 
circle  into  same  number  of  parts. 

The  circle  whose  radius  is  A  D,  is  to  be  divided  into 
eleven  parts.  Set  the  bevel  to  5f  inches  on  blade  of  square 
and  3  inches  on  tongue,  proceed  as  before,  cutting  point  4  on 
Fig.  43  ;   P  4  will  then  be  length  of  chord  required. 

The  circle  having  radius  A  C,  is  to  be  divided  into  thirteen 
parts  ;  we  set  blade  of  bevel  on  6  inches  on  blade  of  square, 
and  3^  inches  on  tongue,  and  proceed  as  before.  Cut  the  line 
at  3  and  P  3  will  be  the  chord  sought  for,  being  1-13  the 
circumference  of  circle. 

The  inner  circle  described  with  radius  A  B,  is  divided  into 
seventeen  parts  as  follows  :  Set  bevel  to  6  inches  on  blade  of 
square,  and  2J  inches  on  tongue  ;  set  to  B  on  Fig.  43,  and 
place  straight  edge  against  blade  cutting  the  line  P  3,  then 


AND     THEIR     USES. 


57 


P  3  at  3  will  be  the  chord  sought.  This  distance  stepped 
round  the  circle  A  B  will  divide  it  thirteen  times. 

This  problem,  or  rather  rule,  may  be  worked  to  any  extent 
and  the  operator  will  soon  find  the  figures  to  make  any  number 
of  divisions  he  may  require. 

Figure  45  shows  a  method  of  constructing  two  unequal 


K  Fig.   45. 

squares  so  that  the  surface  of  the  larger  shall  be  double  that 
of  the  smaller.  Let  A  B  C  D  be  a  square  of  any  size.  Draw 
from  B  through  D,  and  from  C  through  A ;  make  L  H  and 
L  K  equal  B  D  and  A  C  ;  completing  the  other  sides  with 
the  square  as  shown,  then  the  square  L  H  N  K  is  just  twice 
as  large  as  A  B  C  D. 

This  is  a  very  useful  problem  and  may  be  brought  into  use 
by  the  active  workman  in  the  solution  of  many  things  that 
present  themselves  from  time  to  time. 


58  STEEL      SQUARES 

Suppose  we  have  a  post  4x4  inches  supporting  a  given 
weight,  and  we  wish  to  replace  it  with  another,  which  is 
required  to  sustain  double  the  weight,  we  simply  form  a 
square  4x4  inches,  and  proceed  as  shown  in  the  diagram, 
and  the  larger  square  is  the  sectional  area  of  the  required  post 
or  column. 

Of  course  this  may  be  solved  in  a  somewhat  simpler 
manner,  either  with  or  without  the  square.  It  will  be  seen 
on  examination  of  the  diagram  that  it  is  the  diagonal  or  the 
line  running  across  the  corners  of  the  smaller  square  that 
gives  the  sides  of  the  larger  one  ;  hence,  simply  measuring 
across  the  corners  with  a  rule  will  give  the  length  of  side,  or 
by   using  the   square  and  measuring  across,  at  the   figures 


Fig.  46. 

representing  the  size  of  the  smaller  square  ;  for  example,  as 
in  the  post  mentioned,  measure  from  4  inches  on  blade  to 
4  inches  on  tongue,  and  so  on  for  any  dimensions  within  the 
scope  of  the  square.  Reduction  of  sizes  may  be  found  by 
simply  reversing  the  rule,  indeed,  the  thinking  workman  will 
find  in  his  experience  dozens  of  cases  where  this  rule  may  be 
of  use  in  some  form  or  other. 

Figure  46  shows  how  the  circumference  of  a  circle  may  be 
obtained  by  the  square,  the  diameter  being  given.  The  solu- 
tion of  this  problem  by  the  use  of  the  steel  square  has  been 


AND      THEIR      USES.  59 

attempted  by  a  number  of  writers  on  carpentry.  Payne, 
Nicholson  and  Robert  Riddell  have  all  tried  their  hands  at 
it,  besides  a  number  of  lesser  lights,  with  varying  success. 
Riddell,  perhaps,  came  the  nearest  to  a  correct  solution. 
It  is  not  claimed  that  absolute  correctness  is  obtained  in  this 
way,  but  it  is  claimed  for  this-^method  that  it  is  the  nearest 
approach  to  correctness  Vi&tr'm ad e  by  using  the  steel  square. 
The  method  is  not  Wew,  it  having  been  employed  for  more 
than  ten  years.  Let  A.  D  represent  a  straight  edge  of  a  board, 
say  I  o  in.  or  12  in.  wide  ;  place  the  end  of  the  blade  of  square 
at  A,  and  let  D  on  tongue  be  7  15-32  inches.     Take  three 


Fig.  47- 

diameters  from  A  to  C,  and  square  down  a  line  from  C,  cutting 
A  D  at  E  ;  then  A  E  equals  the  circumference.  A  circle  whose 
diameter  is  eight  inches  would  have  a  circumference  equal  to 
the  line  from  A  to  D  by  this  rule.  It  will  be  seen  by  this  that 
any  right  angle  whose  base  is  24,  and  having  an  altitude  of 
7  15-32,  forms  a  constant  by  which  siny  circumference  may  be 
obtained  by  spacing  three  times  the  diameter  on  the  line  A  B, 
and  squaring  down  as  at  C,  the  hypothenuse  being  the  required 
answer.  The  line  A  B  may  be  continued  indefinitely,  being 
careful  to  retain  the  proper  angle  as  shown  in  diagram. 

Fig.  47  shows  a  method  by  which  the  circumference  of  a 
circle  may  be  obtained  from  the  diameter.     This  will  be  found 


6o 


STEEL      SQUARES 


very  convenient  in  almost  all  the  trades  ;    particularly  is  it  so 
for  sheet-metal  workers,  carpenters,  plasterers  and  coopers. 

Describe  a  circle  in  some  proportion  to  the  actual  work, 
say  one  inch  to  the  foot ;  then  apply  the  heel  of  the  square  at 
the  centre  of  the  circle,  as  at  A  ;  then  project  the  lines  A  B 
and  A  C  as  shown.  Now  connect  the  points  where  the  radial 
lines  touch  the  circle  by  the  line  B  C,  and  from  the  middle 
point  of  this  line  draw  the  line  D  E  to  the  circumference. 
To  obtain  the  circumference  of  the  circle,  add  to  three  times 


Fig.  48. 

the  diameter  the  distance  D  E,  which  will  give  the  desired 
result  practically  correct. 

At  Fig.  48  I  give  a  practical  illustration.  Suppose  we  have 
a  circular  tank  or  cistern,  or  a  sheet  metal  vessel  of  any  sort 
that  requires  to  be  eight  feet  in  diameter.  Draw  a  circle  eight 
inches  in  diameter.  This  is  one  inch  to  the  foot ;  place  the 
square  with  the  heel  on  the  centre  as  at  A,  draw  lines  along 
side  blade  and  tongue  as  shown,  cutting  circumference,  then 
at  the  junction  of  these  lines  draw  a  line  same  as  B  C  in  Fig. 


AND      THEIR     USES.  6l 

47,  then  draw  the  short  line  from  the  centre  of  the  line  B  C 
Fig.  47  and  you  have  the  circumference  near  enough  for  all 
practical  purposes.  It  will  be  seen  at  once  how  useful  this 
method  may  prove  to  the  mechanic,  and  how  easily  applied. 
For  getting  the  length  of  hoops,  or  the  number  and  breadth 
of  staves  for  a  circular  tub,  it  will  prove  quite  a  useful 
method. 

At  Fig.  49  is  shown  a  diagram  from  which  the  different 
angles — in  degrees — are  shown  in  such  a  manner  as  to  be 
obtained  at  once  by  the  square.  The  figures  in  the  left 
column  give  the  angles  in  degrees  from  5°  to  90°.  The 
column  on  the  right  shows  the  figures  in  inches,  so  as  to 
enable  the  operator  to  get  the  different  pitches.  For  example, 
if  quarter  pitch  is  wanted  take  12  in.  on  the  blade  and  6  in. 
on  the  tongue,  as  shown  in  the  sixth  space  of  the  column, 
counting  from  the  top.  If  you  want  degrees,  say  for  example 
a  pitch  of  30°,  take  12  in.  on  the  blade  and  6  15-16  on  the 
tongue  and  the  line  along  the  blade  will  have  an  inclination 
of  30°,  and  the  angle  on  the  line  of  the  tongue  will  be  60°. 
This  diagram  will  often  be  found  useful  to  the  carpenter  and 
joiner  in  obtaining  degrees,  for  as  a  rule  a  protractor  is  seldom 
found  in  a  workman's  kit. 

Fig.  50  shows  a  method  of  squaring  the  circle,  which  may 
be  of  use  occasionally.  Erect  a  perpendicular  as  shown  in 
diagram  at  A  B,  then  from  the  centre  of  the  circle  D  space  off 
any  distances  of  equal  length,  as  at  A  and  B.  Use  A  as  a 
centre  and  draw  the  arcs  5  and  6,  then,  using  B  for  a  centre, 
draw  the  arcs  7  and  8,  then  draw  line  C  C,  cutting  centre  of 
arcs  and  running  through  centre  of  circle  at  D.  The  lines 
from  I,  2,  3,  4,  as  shown,  will  square  the  circle.  The  cir- 
cumference may  be  described  before  or  after  the  operation  of 
squaring. 


62 


STEEL     SQUARES 


Hip,  Valley,  Mansard  and  Other  Roofs.^k  work  of  this 
kind  would  not  be  complete  if  it  did  not  embrace  something 
in  regard  to  hip  roofs,  therefore  I  deem  it  proper  to  insert  a 
few  examples  of  roofs  of  this  kind,  showing  how  the  bevels  and 


lines  for  working  out  same  may  be  obtained.  The  question 
of  hip  roofs  was  pretty  thoroughly  discussed  in  the  first  volume 
of  The  Steel  Square  and  its  Uses,  also  my  work  on  Prac- 
tical Carpentry,  so  I  will  only  give  here  a  few  examples  that 
are  not  included  in  the  works  mentioned. 


AND     THEIR     USES.  63 

T0  cut  a  Purlin  against  a  Valley  Rafter.— Lti  ABC  (Fig. 


Fig.  50- 

51)  be  the  eaves  of  the  roof,  D  F  and  F  E  the  ridges,  B  F  the 

F      J 

D 


Fig.  51* 


,alle5r  on  plan,  H  E  the  rise  pf  the  roof,  and  B  E  the  pitch  of 


64 


STEEL  SQUARES 


the  roof.  From  B  describe  the  arc  E  I ;  draw  I  J  parallel  to 
H  F,  and  draw  B  J  ;  then  the  bevel  C  B  J  will  apply  on  the 
top  of  valley. 

From  H  draw  H  K  square  to  B  E,  and  from  H  describe 
the  arc  K  L  ;  draw  K  N  and  L  M  parallel  to  H  F,  and  draw 
N  M  parallel  to  F  D  ;  draw  M  F,  then  the  bevel  L  M  F  will 
apply  on  the  side  of  the  valley. 

At  Fig.  52  I  show  another  method  of  finding  the  bevels. 


Fig.  52. 

Let  A  B  C  be  the  eaves  of  roof,  D  F  and  F  E  the  ridges, 
B  F  the  valley  or  plan,  H  E  the  pitch  of  roof.  Mark  the 
purlin  I  J  K  to  a  large  scale — full  size,  if  possible — and  draw 
I  L,  J  M,  and  K  N  all  parallel  to  E  F ;  make  M  O  equal  to 
J  K  ;  draw  O  P,  and  draw  N  P  parallel  to  D  F  ;  join  M  P  ; 
and  the  bevel  J  M  P  will  apply  on  the  side  of  valley.     Make 


AND     THEIR      USES. 


65 


S  R  equal  to  J  I ;  draw  L  R ;  join  MR;  and  the  bevel  J  M  R 
will  apply  on  top  of  valley. 

The  method  given  here  will  apply  to  hips  as  well  as  valleys, 
and  the  square  may  be  used  in  finding  the  angles  where  the 
pitches  are  given.  It  is  better,  however,  in  cases  of  this  kind, 
to  work  out  the  bevels  and  angles  by  diagrams  as  shown  in  the 
two  figures,  as  it  saves  time  and  insures  accuracy. 

To  Timber  a  Hexagon  Roof. — On  the  line  i  2,  Fig.  53, 


Fig-  53. 

is  the  seat  of  the  hips,  3  4  will  be  the  rise.  On  the  line  i  S, 
say  at  O,  draw  a  line  touching  the  line  i  2  square  from  i  S, 
which  is  the  seat  of  a  jack  rafter.  Make  P  H  equal  P  F ; 
square  from  O  P  draw  the  line  O  H  :   this  gives  the  bevels 


66  STEEL      SQUARES 

and  length  for  plumb  cut  of  jack  rafter.  From  C  7  draw  the 
line  8  9  indefinitely ;  set  the  compasses  to  i  4  and  from  the 
point  4  intersect  9  8.  Repeat  from  7  8,  which  is  the  covering 
for  one  side  of  roof,  the  intermediate  lines  being  the  lengths 
of  jack  rafters  and  bevels  for  side-cut.  On  the  line  i  2,  say 
at  B,  take  B  for  a  centre,  touching  the  line  4  2,  for  radius, 
describe  the  arc  B  C,  through  B,  at  right  angles  to  i  2,  draw 
the  line  D  E,  and  from  C  to  E  and  C  to  D  will  be  found  the 
bevels  for  backing  of  the  hips. 

This  rule  will  apply  to  any  sort  of  a  roof  having  its  plates 
on  the  same  plane,  and  is  particularly  adapted  to  polygons  of 
any  kind.  The  method  is  an  old  one,  having  been  invented 
by  Peter  Nicholson,  from  whose  works  this  and  the  two  pre- 
vious examples  are  taken.  It  will  be  new  to  many  of  my 
readers,  for  I  have  never  seen  it  reproduced  in  any  American 
work  or  publication.  It  is  exceedingly  simple  and,  withal, 
accurate. 

Fig.  54  illustrates  a  very  thorough  and  simple  manner  of 
obtaining  the  lines,  cuts  and  bevels  for  a  Hip  roof  Suppose 
the  lines  A  B  and  B  C  represent  the  walls  at  the  angle  of  a 
building  :  B  E  shows  the  seat  of  the  hip  rafter,  and  G  F  the 
seat  of  a  jack  rafter.  Draw  E  H  at  right  angles  to  B  E,  and 
make  it  equal  to  the  rise  of  the  roof;  join  B  and  H,  and  H  B 
will  be  the  length  of  the  hip  rafter,  and  the  bevel  shown  on  the 
lines  E  H  and  H  B  will  be  the  plumb  cut  for  same.  Through 
E  draw  D  I  at  right  angles  to  B  C ;  upon  B,  with  the  radius 
B  H,  describe  the  arc  H  I,  cutting  D  I  in  I  ;  join  Band  I,  and 
extend  G  F  to  meet  B  I  in  F ;  then  G  J  will  be  the  length  of 
the  jack  rafter.  The  length  of  each  jack  rafter  is  found  in  the 
same  manner  by  extending  its  seat  to  cut  the  lines  B  I.  From 
F  draw  F  K  at  right  angles  to  F  G,  also  F  L  at  right  angles  to 
B  E ;  make  F  K  equal  to  F  L  by  the  arc  L  K,  or  make  G  K 


AND      THEIR      USES. 


67 


equal  to  G  F  by  the  arc  F  K  ;  then  the  angle  at  F  will  be  the 
top  bevel  of  the  jack  rafters  and  the  bevel  at  K  will  be  the 
plumb  cut. 

Valley  rafters  and  "cripples"  connected  with  them  may 
all  be  obtained  by  this  same  method.  This  method  will  apply 
to  any  sort  of  hip  roof,  be  the  angles  right,  acute  or  obtuse, 
with  very  slight  variation  of  lines. 


I  introduce  at  this  point  a  piece  of  pyramidal  frame  work, 
or  battered  frame  work,  as  some  carpenters  term  it.  Since 
sending  out  the  first  volume  of  The  Steel  Square  and  its 
Uses,  I  have  had  hundreds  of  letters  asking  questions  about 
this  kind  of  a  structure  and  for  information  regarding  the 


68  STEEL      SQUARES 

manner  of  construction.  I  have  also  received  many  letters 
asking  for  more  information  regarding  the  manner  of  con- 
structing hip  roofs  and  the  lines  for  splayed  work,  such  as 
hoppers,  carriage  seats  and  similar  work.  All  this  class  of 
work  is  based  on  one  principle,  of  which  the  pyramid  is  the 
central  example. 


Fig.  55- 

If  the  young  workman  wishes  to  grasp  the  hard-pan  prin- 
ciples that  underlie  this  question  or  questions,  let  him  make 
a  rough  pyramid,  say  with  a  base  4x4  feet  on  the  ground 
plan,  and  2x2  feet  at  the  top,  and  four  feet  high.     Now  try 


ANDTHEIRUSES.  69 

and  fit  a  base  board  around  this  pyramid.  Make  one  corner 
a  butt  joint ;  see  that  it  fits  accurately.  This  will  give  an  idea 
of  what  is  wanted,  and  if  careful  notice  is  taken  of  this  joint, 
the  workman  will  be  better  able  to  understand  anything  I  may 
say  on  the  subject  in  hand. 

After  making  a  good  butt  joint  and  finding  out  the  "  why 
and  wherefore"  of  the  change  in  angles  of  a  perpendicular 
base  and  an  inclined  base  in  the  "butts,"  a  mitre  joint  should 
be  tried,  which  will  further  enlighten  the  student. 

The  young  man  who  tries  this  once,  and  thoroughly  investi- 
gates the  operation  and  examines  closely  the  difference  between 
splayed  and  square  work,  will  never  be  at  a  loss  to  make 
a  hopper,  put  on  a  hip  roof,  or  erect  a  tapering  structure 
similar  to  that  shown  at  Fig.  55,  for  hoppers  and  tapering 
structures  are  hip  roofs,  and  hip  roofs  are  perfect  hoppers 
inverted,  or  a  hopper  is  a  part  of  a  hip  roof  inverted,  which- 
ever you  will. 

Fig.  55  shows  a  side  of  a  frame  suitable  for  a  windmill  or 
for  other  similar  purposes.  The  posts  incline  two  inches  to 
the  foot^that  is,  two  inches  from  the  plumb  line  to  every  foot 
in  the  length  of  the  post,  and  this  incline  is  both  ways.  The 
length  of  post  and  bevels  at  the  foot  and  top  of  posts  may  be 
found  by  applying  the  square  as  shown  at  R — that  is,  24  in. 
on  the  blade  and  4  in.  on  the  tongue,  or  2  in.  on  the  tongue 
and  12  in.  on  the  blade,  which  is  the  same  thing,  so  far  as  the 
bevels  are  concerned.  These  same  figures  also  answer  for  the 
ends  of  the  joists,  S  S.  I  show  at  Fig.  56  the  manner  in  which 
the  bevels  at  the  foot  of  the  post  are  marked.  The  dotted  lines 
show  the  bevels  on  all  sides,  for,  as  the  post  leans  two  ways, 
the  post  must  be  beveled  two  ways.  This,  of  course,  will 
present  itself  to  the  workman  as  he  proceeds.  Let  us  suppose 
the  foot  of  the  post  to  have  no  tenon,  but  is  intended  to  rest 


70 


STEEL     SQUARES 


flat-footed  on  the  sills.  This  being  the  case,  it  gives  us  an 
opportunity  of  getting  the  backing  of  the  post,  for,  like  a  hip 
rafter — which  it  is — it  requires  to  be  backed,  if  it  is  intended 


Fig.   56. 

to  be  enclosed  or  boarded,  and  we  will  suppose  it  is  so 
intended.  From  an  examination  of  Fig.  57  we  can  see  how 
the  backing  of  the  post  may  be  obtained  by  using  the  square 


Fig.  57- 

and  applying  it  on  the  foot  after  it  has  been  beveled.  The 
overwood  at  E  is  to  be  removed.  It  will  be  noticed  that  the 
square  is  placed  on  the  angles  O  and  P,  with  its  heel  at  E. 
The  distance  from  E  to  P  is  the  same  as  from  E  to  O.      The 


ANDTHEIRUSES.  71 

overwood  shown  in  this  is  somewhat  exaggerated  purposely, 
to  give  a  clear  idea  of  the  requirements.  The  braces  shown 
in  this  sketch  will  give  the  student  an  opportunity  to  figure. 
The  lengths  and  bevels  may  be  obtained  either  by  using  the 
square  or  by  taking  them  from  a  drawing,  or  by  calculation. 

I  may  observe  at  this  point,  that  the  posts  in  this  structure 
are  simply  like  the  hips  in  a  very  steep  roof  or  spire,  and  may 
be  treated  as  such,  and  the  angles  and  backing  can  be  obtained 
in  the  same  manner.  A  very  full  and  clear  explanation  of 
forming  hip  roofs  is  given  in  ^'Practical  Carpentry,"  pub- 
lished by  the  same  Company  that  publish  this  work  ;  but  to 
insure  the  student's  possession  of  the  practical  rules  required 
to  build  hip  roofs  of  every  description,  I  have  embodied  in  this 
work  a  number  of  excellent  rules  for  that  purpose. 

Mansard  Roofs. — I  have  frequently  been  asked  to  show 
how  the  cuts  and  lengths  of  the  corners  and  rafters  of  a  Man- 
sard or  French  roof  may  be  obtained.  I  herewith  exhibit  a 
method  of  finding  the  lengths  and  bevels  of  a  curved  roof,  with 
the  manner  of  construction,  style  and  method  of  attaching 
cornice,  and  rule  for  getting  curve  of  angle  rafter  :  Suppose 
A  D  to  be  the  seat  line  (Fig.  58),  A  being  the  lowest  point  of 
curve,  draw  X  Y  parallel  to  A  D  ;  at  right  angles  to  A  D  draw 
A  W,  F  N,  G  O,  H  P,  J  Q  and  K  L ;  make  Y  Z  equal  W  Q  ; 
place  the  thickness  of  the  angle  rib  as  shown  at  M  X  ;  at  right 
angles  to  IM  L  draw  L  V,  Q  U,  P  T,  O  S  and  N  R  ;  make  N 
R  equal  to  E  F  ;  make  O  S  equal  B  G  ;  make  P  T  equal  C  H, 
and  Q  U  equal  D  J  ;  through  U  T  S  R  M  trace  the  curve  of 
the  angle  rib  ;  make  U  V  equal  J  K.  The  position  of  the 
upper  and  lower  plates  in  connection  with  the  angle  rib  is 
shown  at  V  and  2.  These  ribs  may  be  got  out  of  plank  ten 
inches  wide,  as  the  curvature  takes  but  six  inches  from  the 

^lS3 


72 


STEEL     SQUARES 


width.     Although  the  radius  for  the  curve,  20  feet,  is  given 
yet  for  all  practical  purposes  the  curve  of  the  rib  may  be  made 


RADIUS  20  Ft. 


Fig.  58. 


by  first  laying  out  the  plank,  as  it  connects  with  cornice  plates 
and  rafter,  then  bending  a  rod  and  marking  the  curve  from 


AND     THEIR     USES.  73 

the  points  given  to  the  depth  3,  4,  as  required.  If  the  angle 
rib  is  drawn  and  placed  as  here  shown  it  will  not  require  to  be 
backed  ;  but  if  for  any  reason  backing  the  rib  is  required,  the 
rule  for  finding  the  lines  for  this  purpose  may  be  found  under 
the  head  of  Hip  Roofs.  A  Mansard  roof  is  really  a  hip  roof  as 
far  as  it  goes,  or  it  may  be  called  an  inverted  hopper,  and,  as 
both  these  questions  are  considered  in  this  work,  it  is  quite 
unnecessary  to  say  more  on  these  matters  here. 

It  will  be  seen  on  examination  of  the  diagram  that  the 
bevel  may  be  obtained  by  the  square,  though  really  there  is 
not  much  gain  in  time  by  using  it  for  this  kind  of  work, 
though  I  might  say  that  in  some  cases,  particularly  when  the 
rafter  is  not  curved,  the  square  may  be  applied  to  advantage. 

Figure  59  shows  another  style  of  French  roof  with  only  a 
portion  of  the  rafter  curved,  it  also  shows  full  details  of  con- 
struction both  of  roof  and  cornice.  In  this  instance  the  curved 
part  of  the  rafter  may  be  nailed  on  as  shown  at  A  B.  CD  shows 
the  side  of  the  rafter.  The  same  method  may  be  observed 
at  the  angle  rib  E  F,  which  may  be  nailed  to  the  hip  H  G. 
The  rules  given  in  the  previous  illustration  are  applicable  to 
this.  The  radius  shown  is  given  here  merely  as  an  example. 
Any  radius  may  be  used. 

Figure  60  shows  a  very  useful  form  of  roof  plan,  with  a 
method  of  finding  the  butt  joint  for  the  straining  beam  and 
principal.  The  line  O  O  is  the  line  of  joint.  A  A  show  how 
the  square  is  applied  ;  the  points  A  A  are  equi-distant  from  S, 
through  which  point  the  joint  line  is  drawn,  having  the  point 
at  the  heel  of  the  square  in  line. 

Concerning  Hopper  Bevels. — Since  the  first  volume  of  The 
Steel  Square  and  its  Uses  was  published  I  have  had  quite  a 
number  of  inquiries  regarding  Fig.  ^Z  of  the  first  part  and  the 
explanation  thereto. 


.--^ 


Fig.  59. 


AND     THEIR     USES. 


75 


It  appears  the  explanation  is  not  sufficiently  clear  to  enable 
all  minds  to  grasp  it,  yet  it  is  simple  and  to  my  mind  the  best 
method  ever  produced  for  obtaining  the  bevels  of  all  ordinary 
hoppers.  I  reproduce  it  in  this  volume  with  a  more  lengthy 
explanation,  and  give  some  examples  so  that  the  workman 
may  more  readily  see  how  to  apply  the  method. 

In  Fig.  6 1  the  whole  thing  may  be  worked  out.  Let  S  S 
be  the  edge  of  a  board  any  width,  and  O  O  the  other  edge  of 
the  board.     Make  the  line  A  B  the  same  bevel  as  the  flare  of 


Fig.  60. 

the  hopper  desired.  Place  the  square  with  the  blade  so  as  to 
coincide  with  the  line  A  B,  and  mark  by  the  tongue  the  line 
B  C,  as  shown,  then  square  up  from  the  edge  of  the  board  the 
line  B  D. 

Now  we  have  a  figure  that  will,  when  properly  applied  by 
the  steel  square,  give  the  cuts  for  a  hopper  of  any  flare,  either 
with  butt  or  mitre  joints. 

Suppose  A  B  to  be  8J  inches,  then  B  C  will  be  12 J  inches 
and  A  D  10  inches  and  D  C  5  inches.  Now  A  B  or  8|  inches 
on  the  blade,  and  A  D  or  10  inches  on  the  tongue,  will  give 


16 


STEEL     SQUARES 


bevel  for  face  cut ;  this  seems  self-evident.  Now  take  B  C  or 
12J  inches  on  the  blade,  and  A  D  or  10  inches  on  tongue  and 
you  have  the  mitre  cut.  Again  take  D  C  or  5  inches  on 
blade,  and  A  D  or  10  inches  on  tongue  and  you  have  the  butt 
cut. 

This  is  an  example  only  and  any  style  of  hopper  built  at 
right  angles  on  its  base,  and  having  sides  of  equal  flare,  may 
have  all  its  cutting  angles  found  by  this  method.  Let  A  B 
always  be  the  guiding  line,  and  the  one  from  which  all  the 
others  take  their  positions,  making  that  line  equal  in  length 
the  width  of  the  side  of  intended  hopper. 


Fig.  61. 

I  recapitulate  the  rule  : 

To  find  bevel  to  cut  across  face  of  board  :  Take  A  B  on 
blade  and  A  D  on  tongue  ;  bevel  of  tongue  is  line  required. 

To  find  mitre  :  Take  B  C  on  blade  and  A  D  on  tongue  ; 
line  of  tongue  is  bevel  sought. 

For  butt  joint :  Take  D  C  on  blade  and  A  D  on  tongue, 
and  line  of  tongue  gives  joint  required. 

I  now  exhibit  a  method  of  obtaining  the  bevels  for  a  hopper 
having  diff'erent  flares  : 

The  rise  to  the  foot  being  given,  find  the  bevels  of  the 
opposite  sides  having  the  lesser  rise  to  the  foot.  Apply  the 
square  to  a  straight-edge,  taking  1 2  in.  on  the  blade  and  the 


AND      THEIR      USES. 


n 


lesser  rise  to  the  foot,  on  the  tongue.  Mark  by  the  blade,  A  B, 
Fig.  62,  make  B  C  perpendicular  to  A  C  D,  and  equal  to  the 
greater  rise  to  the  foot.  Draw  B  D  perpendicular  to  A  B. 
Apply  the  square  to  the  line  A  C  D.  Taking  A  C  on  the 
blade  and  1 2  in.  on  the  tongue,  mark  by  the  blade  for  C  E. 
Make  D  E  perpendicular  to  A  C  D.  Apply  the  square  to  the 
line  A  C  D,  taking  A  B  on  the  blade  and  1 2  in.  on  the  tongue, 
which  will  denote  the  surface  bevel.  Apply  the  square,  taking 
B  D  on  the  blade  and  D  E  on  the  tongue,  which  will  give  the 


line  for  mitre  joint.  For  butt  joints  take  B  D  on  the  blade 
and  1 2  in.  on  the  tongue,  which  will  give  the  bevel  required. 

The  same  results  may  be  obtained  by  geometrical  con- 
struction. 

Make  B  D,  Fig.  62,  equal  to  12  in.  Draw  A  F.  Make 
B  G  equal  to  B  D,  and  draw  F  G.  Make  D  H  equal  to  B  D, 
and  draw  E  H.  Then  the  acute  angle  at  F  is  the  angle  of  the 
surface  bevel,  and  the  obtuse  angle  at  F  is  the  bevel  for  butt 
joints. 

The  angle  E  is  the  bevel  for  mitre  joints. 

To  find  the  bevels  of  the  opposite  sides  having  the  greater 
rise  to  the  foot,  proceed  in  the  same  manner,  being  careful  to 


yS  STEEL      SQUARES 

supersede  lesser  rise  for  greater  rise,  and  greater  rise  for  lesser 
rise. 

The  principles  involved  in  the  foregoing  examples  cover 
the  whole  field  of  hopper  cuts,  and  their  study  is  as  interesting 
as  instructive. 

In  connection  with  the  subject  of  hoppers,  I  present  the 
following  illustration,  Fig.  6^,  taken  from  ''Carpentry  and 


Fig.  63. 


Building.  "  This  shows  how  the  butt  cut  for  any  sort  of  a 
regular  hopper  may  be  cut  by  those  having  a  band-saw  at  their 
disposal. 

It  is  perhaps  more  curious  than  available. 

In  order  to  make  this  department  complete,  I  herewith 
give  a  method  by  which  the  cuts  or  bevels  may  be  obtained 
for  a  flaring  hopper  having  only  three  sides.  In  other  words. 
Fig.  64  gives  bevels  for  a  box  whose  top  and  bottom  form  two 
unequal  equilateral  triangles  : 

Make  the  triangle  C  E  F,  then  from  the  middle  point  of 
E  F  let  fall  the  perpendicular  B  D,  then  draw  A  B  parallel 
and  equal  to  C  D,  also  A  C  parallel  and  equal  to  B  D,  thus 
forming  the  rectangle  A,  B,  C,  D.  Now  draw  C  H  to  the 
same  inclination  from  C  D,  that  a  side  pf  the  box  when 


AND      THEIR      USES. 


79 


finished  will  show  from  the  perpendicular  line  ;  then  draw 
L  D  perpendicular  to  C  H,  and,  with  C  as  a  centre  and  a 
radius  C  L,  make  an  intersection  at  I,  and  connect  I  and  A, 
and  at  A  is  the  bevel  for  the  mitre  at  the  ends.  Again,  with 
D  for  a  centre  and  a  radius  D  L,  make  an  intersection  at  K, 
and  connect  K  and  B  ;  and  at  B  is  the  bevel  for  the  down  or 
cross  cut. 

To  find  the  Bevels  required  to  Mitre  together  the  Flared  Sides 
of  a  Hexagonal  Box, — Let  N  E  (Fig.  65)  be  in  the  plane  of 


ihe  bottom  of  the  box,  and  E  J  the  inclination  of  the  sides  ; 
continue  G  D  to  B  indefinitely  ;  through  J  draw  J  O  parallel 
to  Q  D  ;  through  O  draw  A  C  at  right  angles  to  J  O  ;  make 
E  M  equal  E  J  ;  through  M  draw  L  C  parallel  to  Q  D  ;  make 
F  H  equal  F  J  ;  draw  H  A  parallel  to  Q  D  ;  through  F  draw 
F  B  parallel  to  L  C  ;  connect  C  D,  and  the  bevel  at  D  will 
give  the  angle  for  the  face  joint ;  connect  B  A,  and  the  bevel 
at  B  will  give  the  angle  for  the  mitre  on  the  sq'iare  edge. 
This  rule  may  be  applied  to  other  figures,  such  as  pentagons, 
pptagons,  or  other  similar  hoppers,  where  the  flares  are  equal 


8o 


STEEL     SQUARES. 


Sometimes   the   student  may  get  in  a  little  maze  when 
working  out  the  angles  and  bevels  for  hopper  work,  as  the 
operation   is  often   perplexing,  and,   like  the  rules  for  stair- 
building,  requires  patience  and  steadiness.    There  is  no  reason. 


Fig.  65. 

however,  because  of  these  matters  appearing  difficult  at  first, 
that  they  should  not  be  thoroughly  understood  by  any  ordinary 
workman,  after  two  or  three  trials. 


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THE     STEEL    SQUARE     AND     ITS     USES. 

Being  a  Description  of  the  Square  and  Its  Uses  in  Obtaining  the 
Lengths  and  Bevels  of  all  kinds  of  Rafters,  Hips,  Groins,  Braces, 
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Just  the  book  you  want,  if  you  are  going  to  build  a  cheap  and  comfortable  home. 
It  shows  a  great  variety  of  cheap  and  medium-priced  cottages,  besides  giving  a 
number  of  useful  hints  and  suggestions  on  the  various  questions  liable  to  arise  in 
building,  such  as  selections  of  site,  general  arrangement  of  the  plans,  sauatary 
questions,  &c.     Cottages  costing  from  $500  to  $5,000  are  shown  in  considerable  va- 
riety, and  nearly  every  taste  can  be  satisfied. 

The  information  on  site,  general  arrangement  of  plan,  sanatary  matters,  &c.,  is 
worth  a  gi-eat  deal  more  than  the  cost  of  the  book. 

WATER-CLOSETS.—  ^  Historical,  Mechanical,  and  Sanatary 
Treatise. —  By  Glenn  Brown,  Architect;  Associate  American 
Institute  of  Architects. —  Neatly  bound  in  cloth,  gilt  title.     .     $1 

This  book  contains  over  250  engravings,  drawn  expressly  for  the  work  by  the 
author.  The  drawings  are  so  clear  that  the  distinctive  features  of  every  device  are 
easily  seen  at  a  glance,  and  the  descriptions  are  particularly  full  and  thoroui^h.  Every 
known  water-closet  is  fully  described,  and  an  account  given  of  its  qualities,  advan- 
tages, and  defects.  The  paramount  importance  of  this  depai'tment  of  the  construc- 
tion of  our  houses  renders  all  comment  upon  the  value  of  such  a  work  unnecessary. 

PLASTER:  HOW  TO  MAKE  AND  HOW  TO  USE. 

Being  a  Complete  Guide  for  the  Plasterer  in  the  Preparation  and 
Application  of  all  kinds  of  Plaster,  Stucco,  Portland  Cement, 
Hydraulic  Cements,  Lime  of  Tie),  Rosendale  and  other  Cements. 
With  Useful  and  Practical  Information  on  the  Chemistry,Qualities, 
and  Uses  of  the  Various  Kinds  of  Limes  and  Cements. — Together 
with  Eules  for  Measuring.  Computing,  and  Valuing  Plaster  and 
Stucco  Work. —  To  which  is  appended  an  Illustrated  Glossary  of 
Terms  used  in  Plastering,  &c. —  By  Fred.  T.  Hodgson,  author  of 
''The  Builders'  Guide,  and  Estimators'  Pi  ice-Book,"  "Practical 

Carpentry,"&c.— Cloth,  gilt $] 

This  work  is  illustrated  with  numerous  engi-avings  in  tlie  text,  and  three  plates, 
giving  some  forty  figures  of  ceilings,  center-pieces,  cornices,  panels,  and  soffits.  It 
is  an  invaluable  'book  for  plasterers,  bricklayers,  masons,  builders,  architects,  and 
engineers. 

HANDSAWS:   THEIR    USE,  CARE,  AND    ABUSE. 

How  to  Select  and  How  to  File  Them.— Being  a  Complete  Guide 
for  Selecting,  Usinf::,  and  Filing  all  kinds  of  Handsaws,  Backsaws, 
Compass  and  Keyhole  Saws;  Web,  Hack,  and  Butchers'  Saws; 
Showing  the  Shapes,  Forms,  Angles,  Pitches,  and  Sizes  of  Saw- 
teeth suitable  for  all  kinds  of  Saws,  and  for  all  kinds  of  Wood, 
Bone,  Ivory,  and  Metal.— Together  with  Hints  and  Suggestions 
on  the  Choice  of  Files,  Saw-sets,  Filing-clamps,  and  other  matters 
pertaining  to  the  Care  and  Management  of  all  classes  of  Hand 
end  other  Small  Saws.— By  Fred.  T.  Hodgson,  author  of  "The 
Steel  Square  and  Its  Uses," '"  The  Slide-Kule,  and  How  to  Use  It," 
"The  Builders'  Guide,"  "Practical   Carpentry,"  «&c.— Illustrated 

by  over  Seventy-five   Engravings. —  Cloth,  gilt $1 

Tliis  work  is  intended  more  particularly  for  operative  carpenters,  joiners,  cab- 
inet-makers, carriage-builders,  and  woodworkers  generally, amateurs  or  professional?. 


CATALOGUE    OF  INDUSTRIAL  BOOKS. 

THE     PRACTICAL     UPHOLSTERER. 

Giving  Clear  Directions  for  Skillfully  Performing  all  kinds  of 
Upholsterers'  Work  in  Leather,  Silk,  Plush,  Reps,  Cottons,  Vel- 
vets, and  Carpetings. — Also,  for  Stuffing,  Embossing,  Welting, 
and  Covering  all  kinds  of  Mattresses,  &c. —  Rules  for  Measuring 
Valances,  Curtains,  Tapestry,  Window  and  Door  Drapery,  Curtain 
Rods,  Persian  Beds,  Mantel  Drapery,  Lambrequins,  Cushions, 
Floor-Cloths,  Festoon  Blinds  and  Curtain-Hangings,  and  all  kinds 
of  Upholstery. —  Fully  Illustrated  with  Engravings  of  Tools, 
Sketelies  of  Furniture,  and  numerous  full-page  Illustrations  of 
Original  Decorative  Designs. —  By  A  Practical  Upholsterer. 
12mo,  cloth $1 

This  work  contains  a  number  of  original  designs  in  drapery  and  upholstery, 
with  full  explanatory  test,  and  an  immense  number  of  working  illustrations.  It 
gives  a  description  of  tools,  appliances,  and  materials.  It  tells  how  to  upholster 
chairs,  parlor  furniture,  bedroom  furniture,  &c.  It  contains  rules  for  cutting  bed- 
hangings,  window-curtains,  door-hangings,  blinds,  and  for  measuring  and  cutting 
cai'pets.  It  gives  arithmetical  calculations  for  cutting  carpets,  curtains,  &c.,  mantle- 
board  drapery,  festoons,  and,  in  short,  everything  pertaining  to  upholstery. 

There  is  nothing  publislied  in  this  country  that  is  so  thoi'ough  and  complete  in 
the  instructions  given  for  upholstering,  as  this  book.  It  is  invaluable  alike  to  the 
practical  workman  and  the  amateur. 

CABINET-MAKING,   UPHOLSTERING,   FURNITURE. 

Hints  and  Practical  Information  for  Cahinet-ma'kers,  Upholsterers, 
and  Furniture-men  Generally. — Together  with  a  Descripfiou  of  all 
kinds  of  Finishing,  with  Full  Directions  Therefor;  Varnishes, 
Polishes,  Stains  for  Wood,  Dyes  for  Wood,  Gilding  and  Silvering, 
Recipes  for  the  Factory,  Lacquers,  Metals,  Marbles,  &c.;  Pictures, 
Engravings,  &c. —  Cloth,  gilt $1 

This  book  contains  an  immense  amount  of  the  most  useful  information  for 
those  who  are  engaged  in  the  manufacture,  superintendence,  or  construction  of 
furniture  or  woodwork  of  any  kind.  It  is  one  of  the  cheapest  and  best  books  ever 
published,  and  contains  over  one  thousand  hints,  suggestions,  and  methods;  and 
descriptions  of  tools,  appliances,  and  materials.  All  the  recipes,  rules,  and  directions 
have  been  carefully  revised  and  connected  by  practical  men  of  great  experience,  so 
that  they  will  be  found  thoroughly  trustworthy.  It  contains  many  of  the  recipes 
recently  sold  at  from  $5  to  $500. 

THE      WORKSHOP      COM  PANION -Part    I. 

A  Collection  of  Useful  and  Reliable  Recipes,  Rules,  Processes, 
Methods,  Wrinkles,  and  Practical  Hints,  for  the  Household  and 
the   Shop Paper.  35  cents. —  Cloth,  gilt  title,  60  cents. 

This  is  a  book  of  164  closely  printed  pages,  forming  a  dictionary  of  practical 
information  for  mechanics,  amateurs,  housekeepers,  farmers, —  everybody.  It  is 
not  a  mere  collection  of  newspaper  clippings,  but  a  series  of  original  treatises  on 
various  subjects,  such  as  alloys,  cements,  inks,  steel,  signal-lishts,  polishing  mate- 
rials, and  the  art  of  polishing  wood,  metals,  &c.;  varni.«;hing,  gilding,  silvering,  bronz- 
ing, lacquering,  and  the  working  of  brass,  ivory,  alabaster,  iron,  steel,  glass,  &c. 


CATALOaVE    OF  INDUSTRIAL  BOOKS. 


THE      WORKSHOP      COM  PANION -Part     11. 

A  Collection  of  Useful  and  Reliable  Kecipes,  Eules,  Processes, 
Methods,  Wrinkles,  and  Practical  Hints,  for  the  Household  and 
the   Shop Paper,  35  cents. —  Cloth,  gilt  title,  60  cents. 

This  is  an  extension  of  the  first  part,  and  contains  subjects  which  have  not  been 
discussed  in  the  earlier  volume.  These  two  volumes  contain  an  immense  amount 
of  practical  instruction  on  matters  in  regard  to  which  information  is  constantl.v 
desired  by  amateurs  and  practical  men. 

THE    PRACTICAL    ASSISTANT,  AND    WORKSHOP 

COMPANION.— A  Treasury  of  Useful  Information  relating 
to  the  Arts  and  Sciences  of  everyday  life. — Containing  Useful 
and  Reliable  Processes,  Recipes,  Wrinkles,  Methods,  Rules,  Data, 
Tables;  and  Hints  for  the  Factory  and  the  Household,  the  Shop 
and  the  Farm.— Edited  by  John  Phin.— Cloth, $1 

This  is  Parts  I  and  II  of  "The  Workshop  Companion,"  described  above,  hand- 
somely bound  together  in  cloth,  with  gilt  title. 

THE     AMATEURS'     HANDBOOK    OF    PRACTICAL 
INFORMATION,  for  the  Workshop  and  Laboratory, 

Second  Edition.—  Greatly  Enlarged.—  Neatly  bound.  .  .  15  cents. 

This  is  a  handy  little  book,  containing  just  the  information  needed  by  amateurs 
In  the  workshop  and  laboratory.  Directions  for  making  alloys,  fusible  metals, 
cements,  glues,  &c.;  and  for  soldering,  brazing,  lacqueiiug,  bronzing,  staining  and 
polishing  wood,  tempering  tools,  cutting  and  working  glass,  varnishing,  silvering, 
gilding,  preparing  skins,  &e.  The  new  edition  contains  extended  directions  for 
preparing  polishing  powders,  freezing  mixtures,  colored  lights  for  tableaux,  solu- 
tions for  rendering  ladies'  dresses  incombustible,  &c.  There  has  also  been  added 
a  very  large  number  of  new  and  valuable  recipes. 

The  Workshop  Companion,  Part  1,  above  described,  contains  all  the  matter 
that  is  to  be  found  in  "The  Amateurs'  Handbook." 

MECHANICAL     DRAUGHTING. 

The  Student's  Illustrated  Guide  to  Practical  Draughting.— A  series 
of  Practical  Instructions  for  Machinists,  Mechanics,  Apprentices, 
and  Students  at  Engineering  Establishments  and  Technical  In- 
stitutes.—  By  T.  P.  Pemberton,  Draughtsman  and  Mechanical 
Engineer. —  Illustrated  by  numerous  engravings. —  Cloth,  gilt.  $1 
This  is  a  simple  but  thorough  book,  by  a  draughtsman  of  twenty-five  years' 
experience.  It  is  intended  for  beginnei's  and  self-taught  students,  as  well  as  for 
those  who  pursue  the  study  under  the  direction  of  a  teacher. 

DRAWING     INSTRUMENTS. 

Being  a  Treatise  on  Draughting  Instruments,  with  Rules  for  their 
Use  and  Care;  Explanations  of  Scales,  Sectors,  and  Protractors. 
Together  with  Memoranda  for  Draughtsmen;  Hints  on  Purchasing 
Instruments,  Paper,  Ink,  Pencils,  &c.  Also,  a  Price-list  of  all  Mate- 
rials required  by  Draughtsmen. —  Illustrated  with  twenty-four  Explan- 
atory Illustrations.— By  Fred.  T.  Hodgson.— Paper.  ...  25  cents. 


CATALOGUE    OF  INDUSTRIAL  BOOKS. 

THE     SLIDE-RULE,  AND    HOW    TO    USE    IT. 

Being  a  Compilation  of  Explanations,  Rules,  and  Instructions, 
suitable  for  Mechanics  and  others  interested  in  the  Industrial 
Arts. —  Compiled  and  arranged  by  Fred.  T.  Hodgson. — 25  cents. 

Rules  are  given  for  the  measurement  of  all  kinds  of  boards  and  planks,  timber 
in  the  round  or  square,  glaziers'  work  and  painting,  brickwork,  paviors'  work,  tiling 
and  slating,  the  measurement  of  vessels  of  various  shapes,  the  wedge,  inclined  planes, 
wheels  and  axles,  levers,  the  weighing  and  measurement  of  metals  and  all  solid 
bodies,  cylinders,  cones,  globes,  octagon  rules  and  formulae,  the  measurement  of 
circles,  and  a  comparison  of  French  and  English  measures, with  much  other  informa- 
tion useful  to  builders,  carpenters,  bricklayers,  glaziers,  paviors,  slaters,  machinists, 
and  other  mechanics. 

Possessed  of  this  little  book  and  a  good  slide-rule,  mechanics  might  carry  in 
their  pockets  some  liundreds  of  times  the  power  of  calculation  that  they  now  have 
in  their  heads,  and  the  use  of  the  instrument  is  very  easily  acquired. 

THE  ENGINEER'S  SLIDE-RULE,  and  Its  Applications. 

A  Complete  Investigation  of  the  Principles  upon  which  the  Slide- 
Rule  is  constructed;  together  with  the  Method  of  its  Application 
to  all  the  Purposes  of  the  Practical  Mechanic. —  By  William 
TONKES. —  Paper 25  cents. 

THE     LIGHTNING     CALCULATOR. 

Practical  Hints  on  Lightning  Calculating. —  To  which  are  added 
Rules,  Tables,  Data,  Formulae,  and  Memoranda,  for  making  rapidly 
those  everyday  calculations  that  are  required  in  business,  mechan- 
ics, and  agriculture. —  Paper 20  cents. 

A     CENTURY     OF     INVENTIONS. 

An  exact  reprint  of  the  famous  "Century  of  Inventions"  of  the 
Marquis  of  Worcester  (first  published  in  1663). — With  au  Intro- 
duction, Notes,  and  a  Life  of  the  Author. — With  Portrait  after  a 
Painting  by  Van  Dyke. —  Edited  by  John  Phin.— Cloth.    .    .    .   $1 

This  is  one  of  the  most  extraordinary  books  ever  published.  The  famous 
"Century  of  Inventions"  is  of  more  than  mere  historical  interest.  It  contains  nu- 
merous hints  and  suggestions  of  what  might  be  accomplished,  and  will  be  found  of 
great  interest  and  value  to  every  one  interested  in  mechanics.  Many  persons  claim 
that  the  Marquis  of  Worcester  anticipated  many  of  our  most  important  modern 
inventions  and  discoveries.  Great  care  has  been  taken  to  reprodtiee  exactly  (so  far 
as  modern  type,  &e.,  could  do  it)  the  edition  published  by  the  Marqixis  himself.  It 
has  been  entirely  out  of  print  for  many  years. 

THE       ELECTRICIAN'S       POCKET      COMPANION. 

Electrical  Rules,  Tables,  Tests,  and  Formulae.— By  Andrew 
Jamieson,  C.E.,  F.R.S.E.— Fully  illustrated.— Cloth 75  cents. 

This  is  the  most  compact  and  thorough  work  in  the  market  for  the  practical 
eleeti'ieian.  It  contains  minute  directions  for  all  calculations,  tests,  &c.,  with  clear 
engravings  of  the  apparatus  employed.  The  following  list  of  contents  will  give  an 
idea  of  its  scope : — 

Formulae  of  the  Absolute  Units,— Practical,  Electrical,  and  Mechanical. 

Heat  and  Light   Units. 

Electro-chemical  Equivalents,  Electrolysis,  Heat  and  Energy  of  Combustion. 

Practical  Methods  of  Electrical  Measurements. 

Electric  Conductors:    Copper,  &c.— Insulators:   Guttapercha,  &c. 

Submarine   Cables.— Aerial  Land-lines. 

Electric  Lighting,  and  Transmission  of  Power. 


CATALOGUE    OF  INDUSTRIAL  BOOKS. 

LECTURES    IN    A   WORKSHOP -By  t.  p.  Pemberton, 

formerly  Associate  Editor  of  The  Technologist;  author  of  "The 
Student's  Illustrated  Guide  to  Practical  Draughting." — With  an 
Appendix  containing  the  famous  papers  by  Whitworth  ''On  Plane 
Metallic  Surfaces  of  True  Planes";  *'0n  the  Uniform  System  of 
Screw-Threads";  ''Address  to  the  Institution  of  Mechanical  En- 
gineers, Glasgow";  "On  Standard  Decimal  Measures  of  Length." 

Cloth,  gilt $1 

We  have  here  a  sprightly,  fascinating  book,  full  of  valuable  hints,  interesting 
anecdotes,  and  sharp  sayings.  It  is  not  a  compilation  of  dull  sermons  or  dry  math- 
ematics, but  a  live,  readable  book.  The  papers  by  Whitworth,  now  first  made 
readily  accessible  to  the  American  reader,  form  the  basis  of  our  modern  systems  of 
accurate  work. 

THE     NEW     POCKET     CYCLOPEDIA. 

A  Compendium  of  General  Knowledge,  Useful  and  Interesting 
Facts,  Valuable  Statistics,   and  Practical  Information. —  16mo., 

cloth 50  cents. 

This  is  a  handy  volume  of  164  pages,  printed  in  small  but  clear  type  on  very  fine 
thin  paper,  so  that  the  book  may  be  readily  carried  in  the  pocket  or  trunk.  It  con- 
tains all  those  facts  and  figures  which  are  most  commonly  referred  to  in  eveiyday 
life,  great  care  being  taken  to  secure  accuracy  and  clearness.  It  is  not  a  collection 
of  "curious  information"  made  up  from  newspaper  clippings,  but  a  thoroughly 
arranged  manual  of  the  most  useful  general  knowledge. 

HOW    TO     BECOME    A    GOOD     MECHANIC. 

Intended  as  a  Practical  Guide  to  Self-taught  Men:  Telling  What 
to  Study;  What  Books  to  Use;  How  to  Begin;  What  Difficulties 
will  be  met ;  How  to  Overcome  Them.     In  a  word,  how  to  carry 
on  such  a  course   of  self-instruction   as  will  enable   the  young 
mechanic  to  rise  from  the  bench  to  something  higher. — Paper,  15e. 
This  is  not  a  book  of  "goody-goody"  advice,  neither  is  it  an  advertisement  of 
any  special  system,  nor  does  it  advocate  any  hoblay.     It  gives  plain  practical  advice 
in  regard  to  acquiring  that  knowledge  which  alone  can  enable  a  young  man  engaged 
in  any  profession  or  occupation  connected  with  the  industrial  arts  to  attain  a  po- 
sition higher  than  that  of  a  mere  workman. 

CEMENTS,    GLUE,    AND     PASTE. 

A  Practical  Treatise  on  the  Preparation  and  Use  of  all  kinds  of 
Cements,  Glue,  and  Paste. —  By  John  Phin,  author  of  "How  to 

Use  the  Microscope." — Paper 25  cents. 

Every  mechanic  and  householder  will  find  this  volume  of  almost  every-day  use. 

It  contains  nearly  two  hundred  recipes  for  the  preparation  of  cements  for  almost 

every  conceivable  pui-pose. 

HINTS     FOR      PAINTERS,     DECORATORS,     AND 
PAPER-HANGERS. 

Being  a  Selection  of  Useful  Rules,  Data,  Memoranda,  Methods, 
and  Suggestions  for  House,  Sliip,  and  Furniture  Painting;  Paper- 
Hanging,  Gilding,  Color-Mixing,  and  other  matters  useful  and 
instructive  to  painters  and  decorators. —  Prepared  with  special 
reference  to  the  wants  of  amateurs. —  By  An  Old  Hand. — 
Paper 25  cents. 


CATALOGUE    OF  INDUSTRIAL  BOOKS. 


THE     HARDWOOD     FINISHER: 

With  Rules  and  Directions  for  finishing  in  Natural  Colors,  and  in 
Antique,  Mahogany,  Cherry,  Birch,  Walnut,  Oak,  Ash,  Redwood, 
Sycamore,  Pine,  and  all  other  Domestic  Woods.  Finishing,  Filling, 
Staining,  Varnishing,  and  Polishing.  Also,  Miscellaneous  Rules 
for  Dyeing,  Gilding,  and  Bronzing. —  Compiled  and  Edited  by 
Fred.  T.  Hodgson,  late  Editor  of  T}ie  Builder  and  Woodworker, 
and  of  The  Cabinetmaker  and  Upholsterer. —  ]2mo,  cloth.  .     .     $1 

In  this  country  the  art  of  using  wood  for  almost  every  purpose  has  gone  far 
beyond  anj'thing  that  has  ever  been  attempted  by  any  other  people.  The  modera 
houses  of  the  Americans  are  finished  with  a  richness  and  beauty  in  the  woodwork 
of  which  our  fathers,  not  to  speak  of  our  grandfathers,  had  little  idea.  The  car- 
penter, builder,  or  painter  who  does  not  fully  understand  the  best  methods  of 
finishing  the  hard  woods  so  as  to  preserve  and  increase  their  beauty  is  behind  the 
times.  The  object  of  this  book  is  to  aid  him  in  acquiring  the  knowledge  necessary 
to  this  end;  and  the  author  has  certainly  succeeded  in  producing  an  exhaustive 
treatise  on  the  subject. 

THE     ENGINEER'S     HANDY-BOOK: 

Containing  a  series  of  Useful  Calculations  for  Engineers,  Tool- 
makers,  Millwrights,  Draughtsmen,  Foremen  in  Engineering  Es- 
tablishments, and  for  the  better  class  of  Mechanics  and  Artizans 
generally.  Also,  Rules  to  determine  the  Proportion  of  Wheels  for 
Screw-cutting  by  a  Lathe,  &c. —  From  the  fifth  London  edition, 
with  American   additions. —  32mo,  cloth 50  cents. 

PLAIN    DIRECTIONS    FOR    THE 

CONSTRUCTION  AND  ERECTION  of  LIGHTNING- 
RODS. —  ^y  John  Phin,  C.E.,  author  of  "Chemical  History  of 
the  Six  Days  of  Creation,"  "How  to  Use  the  Microscope,"  &c. 
Enlarged  and  fully  illustrated. —  Third  edition. —  12mo,  cloth, 
gilt  title 75  cents. 

This  is  a  well-known  and  standard  work.  It  is  simple  and  pi'actical,  intended 
to  convey  just  such  information  as  will  enable  every  property-owner  to  decide 
whether  or  not  his  buildings  are  thoroughly  protected.  It  is  the  only  book  on  this 
subject  published  in  this  country  that  has  not  been  written  in  the  interest  of  some 
patent  or  some  manufacturing  concern.  By  following  its  directions  any  ordinarily 
skillful  mechanic  can  put  up  a  rod  that  will  afford  perfect  protection,  and  that  will 
not  infringe  on  any  patent.    Every  owner  of  a  house  or  barn  ought  to  procure  a  copy. 

TRADE    "SECRETS"    AND      PRIVATE      RECIPES. 

A  Collection  of  Recipes,  Processes,  and  Formulas  that  have  been 
offered  for  sale  at  prices  varying  from  25  cents  to  $500.  With 
Notes,  Corrections,  Additions,  and  Special  Hints  for  Improve- 
ments.—  Edited  by  John  Phin,  assisted  by  an  experienced  and 
skillful  pharmacist. —  Cloth,  gilt  title 60  cents. 

This  work  was  prepared  by  the  author  for  the  purpose  of  collecting  and  pre- 
senting in  a  compact  form  all  those  recipes  and  so-called  "trade  secrets"  which 
have  been  so  extensively  advertised  and  offered  for  sale.  It  is  by  no  means  a 
claptrap  book,  though  it' exposes  many  claptraps.  It  contains  a  large  amount  of 
valuable  information  that  can  not  be  readily  found  elsewhere ;  and  it  gives  not  only 
the  formulae,  &c.,  for  manufacturing  an  immense  variety  of  articles,  but  important 
and  trustworthy  hints  as  to  the  best  way  of  making  money  out  of  them.  Even  as  a 
book  of  recipes* it  is  worth  more  than  its  price  to  any  one  who  is  interested  in  the 
subject  on  which  it  treats. 


CATALOGUE    OF  IXDUSTBIAL  BOOKS. 
A    PRACTICAL   GUIDE   TO 

SUCCESS     IN     THE      USE     OF     RECIPES, 

Formulae,  &c.,  with  Hints  on  Chemical  and  Mechanical  Manipula- 
tion.—  Intended  as  a  supplement  to   all  books  of  recipes. —  By 

John   Phin. —  12mo,  paper 25  cents. 

While  it  is  an  undoubted  fact  that  many  of  the  recipes  published  in  the  ordinary 
collections  are  erroneous,  either  from  original  blunders  on  the  part  of  the  authors 
or  from  mistakes  in  copying,  failure  in  the  use  of  others  frequently  arises  from 
defective  information  and  vicious  methods  on  the  part  of  those  who  attempt  to  put 
them  in  practice.  The  object  of  the  present  book  is  to  give  such  hints  and  cautions 
as  will  enable  the  worker  to  secure  success  where  success  is  possible ;  and  where 
the  products  are  intended  for  sale  it  gives  special  and  valuable  advice  as  to  the  best 
methods  of  putting  them  on  the  market. 

A    MANUAL    OF    INSTRUCTION    IN 

THE      ART      OF      WOOD       ENGRAVING. 

With  a  Description  of  the  necessary  Tools  and  Apparatus,  and 
Concise  Directions  for  their  Use ;  Explanations  of  the  Terms  used 
and  the  Methods  employed  for  producing  the  various  classes  of 
Wood  Engravings.— By*  S.  E.  Fuller.— Fully  illustrated  -with 
engravings  by  the  author,  separate  sheets  of  engravings  for  trans- 
fer and  practice  being  added. —  New  edition,  neatly  bound.  50  cts. 
A  really  thorough  and  practical  work,  written  for  those  who  want  to  learn  the 
art  without  the  aid  of  a  teacher. 

A     GUIDE     TO      COLLODIO      ETCHING.-By 

Rev.  Benjamin   Hartley. —  Illustrated  by  the   author. —  12mo, 

cloth $1.00 

This  volume  gives  complete  and  minute  instmctions  for  one  of  the  most  delight- 
ful of  amateur  arts.  It  is  fully  illustrated  by  woodcuts  of  all  the  apparatus  used 
(which  is  very  simple  and  easily  made),  and  also  by  actual  photo-prints  of  the 
etchings  themselves. 

THE     PRACTICAL     POCKET     COMPANION. 

A  Cyclopedia  of  the  most  useful  Facts,  Figures,  and  General 
Information  required  by  everybody  in  everyday  life. —  Edited  by 
John  Phin,  author  of  "How  to  Use  the  Microscope,"  "The  Work- 
shop Companion,"  "Chemical  History  of  the  Six  Days  of  Crea- 
tion," &e. —  Numerous  illustrations =     10  cents. 

Contents.— Abbreviations  in  Common  Use— Business  Laws  and  Commercial 
Rules— Acceptances— Agencies— Bills  of  Eschange—Cheeques— Common  Carriers— 
Corporations— Law  of  Finding— Indorsements— Innkeepers— Negotiable  Instruments 
—Partnerships— Promissory  Notes — Protests— Receipts— Concrete  Walls  for  Houses 
—Copyrights— Rules  for  Correspondence— How  to  treat  Accidents  to  the  Eye— Fac- 
tors of  Safety— Best  Methods  of  Extinguishing  Fires— Language  of  Flowers— Sig- 
nificance of  Gems  and  Precious  Stones— Periods  of  Gestation  and  Incubation— Legal 
Holidays— Homestead  Law— Distinguishing  Characteristics  and  Anxious  Periods  of 
Infectious  Diseases— Prevention  of  Attacks  of  Insects— Knots,  and  How  to  Tie 
Them,  with  full  page  of  illustrations— Genei-al  Rules— Single  Draw-knot— Galley- 
knot — Square-knot,  or  Reefing-knot— Weaver's-knot,  or  Sheet-bend-knot— Half  hitch 
—Two  Half -hitches— Clove-hitch— Timber-hitch— Bowline-knot  —  Fisherman's-knot 
—Whipping  or  Binding— Tying  Parcels— Care  of  Leather— Lightning-rods,  general 
rules  for— Best  Materials— Proper  Size  and  Best  Shapes  of  Rod— Painting— Points, 
or  Air-Terminals— Ground  Connections— Arrangement  and  Mode  of  Attaching  the 
Rod  to  the  House— Value  of  Moneys  of  Foreign  Nations— Passports— Patents— Anti- 
dotes for  Poisons— Postal  Rules  aiid  Rates— Railroad  and  Steamboat  Signals— Rules 
for  Spelling  and  the  Use  of  Capitals— Trade-marks— Weather  Indications,  &c. 


CATALOGUE    OF  IIWUSTRTAL  BOOKS. 


WHAT   TO    DO   AND    HOW  TO    DO    IT   IN    CASE 

OF  ACCIDENT.— A  book  for  everybody.— Cloth,  gilt.   50  cts. 

This  is  one  of  the  most  useful  books  ever  published.  It  tells  exactly  what  to 
do  iu  case  of  accidents,  such  as  severe  cuts,  sprains,  dislocations,  broken  bones, 
burns  with  tire,  scalds,  burns  with  corrosive  chemicals,  sunstroke,  suffocation  by 
foul  air,  hanging,  drowning,  frost-bite,  fainting,  stings,  starvation,  lightning,  poisons, 
accidents  from  machinei-y  and  from  the  falling  of  scaffolding,  gunshot  wounds,  &c. 
It  ought  to  be  in  every  house,  for  young  and  old  are  liable  to  accident,  and  the 
directions  given  in  this  book  might  be  the  means  of  saving  many  a  valuable  life. 

COMMON    SENSE    IN   THE    POULTRY-YARD. 

A  Story  of  Failures  and  Successes,  including  a  full  account  of 
1,000  hens  and  what  they  did.    With  a  complete  description  of  the 
houses,  coops,  fences,  runs,  methods  of  feeding,  breeding,  market- 
ing, &c.,  and  many  new  wrinkles   and   economical  dodges. —  By 
J.  P.  Haig. — With  numerous  illustrations.— Cloth,  gilt  title.      $1 
This  is  a  lively  and  entertaining  work,  which  embodies  the  actual  experience  of 
many  years  in  the  keeping  of  poultry  in  large  and  small  numbers.    It  is  the  most 
thoroughly  practical  work  on  poultry  in  the  market,  and  contains  an  amount  of 
solid  information  which,  to  even  the  keeper  of  a  dozen  fowls,  will  make  it  worth 
many  times  its  cost. 

A    DICTIONARY    OF    PRACTICAL     BEE-KEEPING. 

With  Notes  and  Practical  Hints.— By  John  Phin,  author  of 
**How  to  Use   the  Microscope,"  &c. —  Numerous  illustrations. — 

Cloth,  gilt 50  cents. 

This  work  discusses  thoroughly  nearly  five  hundred  subjects.  Gives  in  con- 
densed form  an  immense  amount  of  valuable  information  under  the  different  head- 
ings. Under  the  heads  Bee.  Comb,  Glucose,  Honey,  Race,  Species.  Sugar,  Wax,  and 
others,  it  brings  together  a  large  number  of  important  facts  and  figures  now  scat- 
tered through  our  bee  literature  and  costly  scientific  works,  and  are  not  easily 
found  when  wanted.    Here  they  can  be  referred  to  at  once  under  the  proper  head. 

PLAIN     DIRECTIONS     FOR    ACQUIRING 

THE    ART    OF    SHOOTING    ON    THE    WING. 

With  Useful  Hints  concerning  all  that  relates  to  Guns  and  Shoot- 
ing, particularly  in  regard  to  the  art  of  loading  so  as  to  kill.  To 
which  has  been  added  several  valuable  and  hitherto  secret  recipes, 
of  great  practical  importance  to  the  sportsman. — By  An  Old  Game- 
keeper.—12mo,  cloth 75  cents. 

This  book  contains  a  novel  and  most  valuable  feature  found  in  no  other  work  on 
this  subject.  This  is  a  series  of  graduated  lessons  by  which  the  self-taught  young 
sportsman  is  enabled  to  advance  step  by  step  from  such  easy  marks  as  a  sheet  of  pa- 
per nailed  on  a  fence  to  the  most  difficult  trap-shooting  and  the  sharpest  snap-shots. 

THE    PISTOL  AS    A  WEAPON    OF   DEFENCE, 

In  the  House  and  on  the  Road.— 12mo,  cloth.  ...     50  cents. 

This  work  aims  to  instruct  peaceable  and  law-abiding  citizens  in  the  best  means 
of  protecting  themselves  from  the  attacks  of  the  brutal  and  the  lawless,  and  it  is  the 
only  practical  book  published  on  this  subject.     Its  contents  are  as  follows  :— 

The  Pistol  as  a  Weapon  of  Defence— The  Carrying  of  Firearms— Different  kinds 
of  Pistols  in  Market— How  to  Choose  a  Pistol— Ammunition,  different  kinds :  powder,  . 
caps,  bullets,  copper  cartridges.  &c.  — Best  form  of  Bullet— How  to  Load— Best 
Charge  for  Pistols— How  to  Regulate  the  Charge— Care  of  the  Pistol :  how  to  clean 
it— How  to  Handle  and  Carry  the  Pistol— How  to  Learn  to  Shoot— Practical  Use  of 
the  Pistol— How  to  Protect  Yourself  and  Disable  your  Antagonist. 


CATALOGUE    OF  INDVSTTtlAL  BOOKS. 

CHEMICAL  HISTORY  of  the  SIX  DAYS  of  CREATION 

By  John  Phin,  author  of  "How  to  Use  the  Microscope,"  &c. 
12mo,  cloth 75  cents. 

In  this  volume  an  attempt  is  made  to  trace  the  evolution  of  our  globe  from  the 
primeval  state  of  nebulous  mist,  "without  form  and  void,"  and  existing  in  "dark- 
ness," or  with  an  entire  absence  of  the  manifestation  of  the  physical  forces,  to  the 
condition  in  which  it  was  fitted  to  become  the  habitation  of  man.  While  the  state- 
ments and  conclusions  are  rigidly  scientific,  it  gives  some  exceedingly  novel  views 
of  a  rather  hackneyed  subject. 

THE  SUN:  A  Familiar  Description  of  his  Phenomena. 

By  Rev.  Thomas  William  Webb,  M.A.,  F.R.A.S.,  author  of 
''Celestial  Objects  for  Common  Telescopes." — With  numerous 
illustrations. —  12mo,  cloth 40  cents. 

This  work  gives,  in  a  delightfully  popular  style,  an  account  of  the  most  recent 
discoveries  in  regard  to  the  sun.    It  is  freely  illustrated. 

HOW      TO      USE       THE       MICROSCOPE. 

A  Book  of  Practical  Hints  on  the  Selection  and  Use  of  the 
Microscope.  Intended  for  beginners. —  By  John  Phin,  editor  of 
The  American  Journal  of  Microscopy. —  Sixth  edition.  Greatly 
enlarged,  with  over  eighty  engravings  in  the  text,  and  eight  full- 
page  engravings,  printed  on  heavy  tint  paper. — 12mo,  cloth.    $1.25 

This  work  has  been  received  with  such  general  favor  that  it  has  passed  through 
five  large  editions  in  a  few  years.  It  gives  a  full  account  of  the  different  kinds  of 
microscopes;  of  the  various  accessories,  and  of  the  best  methods  of  using  them; 
of  the  best  methods  of  collecting,  preparing,  and  preserving  objects,  and  preparing 
slides  and  cabinets.  Many  of  the  illustrations,  devices,  and  methods  used,  are 
original  with  the  author,  although  they  have  been  freely  copied  and  appropriated 
without  credit  by  several  other  writers. 

A    BOOK     FOR 

BEGINNERS     WITH     THE     MICROSCOPE. 

Being  an  abridgement  of  ''How  to  Use  the  Microscope." — By 
John  Phin. —  Fully  illustrated,  and  neatly  and  strongly  bound 
in    cloth 50  cents. 

This  book  was  prepared  for  the  use  of  those  who,  having  no  knowledge  of  the 
use  of  the  microscope,— or,  indeed,  of  any  scientific  apparatus, —  desire  simple  and 
practical  insti'uction  in  the  best  methods  of  managing  the  instrument  and  preparing 
objects. 

THE    MICROSCOPE.— By  Andrew  Ross.— Fully  illustrated. 
12mo,  cloth,  gilt  title 75  cents. 

This  is  the  celebrated  article  contributed  by  Andrew  Ross  to  "The  Penny  Cyclo- 
pedia," and  quoted  so  frequently  by  writers  on  the  microscope.  Carpenter  and 
Hogg,  in  the  latest  editions  of  their*  works  on  the  microscope,  and  Brooke,  in  his 
treatise  on  Natural  Philosophy,  all  refer  to  this  article  as  the  best  source  for  full 
and  clear  information  in  regard  to  the  principles  upon  which  the  modem  achromatic 
microscope  is  constructed.  It  should  be  in  the  library  of  every  person  to  whom  the 
microscope  is  more  than  a  toy.  It  is  written  in  simple  language,  free  from  abstruse 
teclmicalities. 


CATALOGUE    OF  INDUSTRIAL  BOOKS. 

THE  ANGULAR  APERTURE  OF  MICROSCOPE 
OBJECTIVES. 

By  Dr.  George  E.  Blackham.—  Eighteen  full-page  illustrations. 
Printed  on  extra  fine  paper. —  8vo,  cloth $1.25 

This  is  the  elaborate  paper  on  Angular  Aperture  read  by  Dr.  Blackham  before 
the  Microscopical  Congress,  held  at  Indianapolis. 

SECTION-CUTTING      FOR      THE      MICROSCOPE. 

A  Practical  Guide  to  the  Preparation  and  Mounting  of  Sections 
for  the  Microscope,  special  prominence  being  given  to  the  subject 
of  Animal  Sections. —  By  Sylvester  Marsh,  M.D. —  Reprinted 
from  the  London  edition. — With  illustrations. —  12mo,  cloth,  gilt 
title 75  cents. 

This  is  undoubtedly  the  most  thorough  treatise  extant  upon  section-cutting 
in  all  its  details.  The  American  edition  has  been  greatly  enlarged  by  valuable 
explanatory  notes ;  and  also  by  extended  directions,  illustrated  with  engi-avings,  for 
selecting  and  sharpening  kuives  and  razors. 

THE       MARVELS       OF       POND        LIFE. 

A  Year's  Microscopic  Recreations  among  the  Polj^s,  Infusoria, 
Rotifers,  Water-Bears,  and  Polyzoa. — By  Henry  J.  Slack,  F.G.S., 
F.R.M.S.,  &c. —  Seven  full-page  plates,  and  numerous  wood  en- 
gravings in  the  text.— Second  edition. —  12mo,  cloth,  gilt.     .    $1 

DIATOMS.— Practical  Directions  for  Collecting,  Pre- 
serving, Transporting,  Preparing,  and  Mounting  Diatoms.— By 
Prof.  A.  Mead  Edwards,  M.D.,  Prof.  Christopher  Johnston, 
M.D.,  PEof.  Hamilton  L.  Smith,  LL.D.— ]2mo,  cloth.     75  cents. 

This  volume  contains  the  most  complete  series  of  directions  for  collecting, 
preparing,  and  mounting  diatoms,  ever  published.  The  directions  given  are  the 
latest  and  best. 

BACTERIA:    FORMS   AND    MODES    OF   GROWTH. 

A  Series  of  Papers  on  the  Exliibits  at  the  Biological  Laboratory 
of  the  Health  Exhibition,  under  the  charge  of  Watson  Cheyne. 
Reprinted  from  the  London  Lancet. —  Illustrated  with  over  thirty 
engravings,  showing  the  forms  and  modes  of  growth  of  the  various 
species,  and  the  apparatus  used  in  the  different  "cultures." — 
12mo,  paper 25  cents. 

TRICHINyC    SPIRALIS:    How  to    Detect  Them   and 

How  to  Avoid  Them.— -^  Popular  Account  of  the  Habits, 
Modes  of  Propagation,  and  Means  of  Dissemination  of  Pork- 
worms  or  Flesh- worms. —  By  John  Phix,  author  of  "How  to  Use 
the  Microscope." — Fully  illustrated. —  Paper.      ,     ,     ,     25  cents. 


CATALOGUE    OF  INDUSTRIAL  BOOKS. 


HANDBOOK    OF     URINARY    ANALYSIS,   Chemical 

and     Microscopical.— For  the  Use    of    Physicians,    Medical 
Students,  and  Clinical  Assistants. —  By  Frank  M.  Deems,  M.D., 
Laboratory  Instructor  in  the  Medical  Department  of  the  Univer- 
sity of  New  York;   Member  of  the   New  York  County  Medical 
Society;   Member  of  the  New  York  Microscopical  Society,  &c. — 
Second  edition. — Greatly  enlarged,  and  fully  illustrated. — Cloth.  $1 
This  manual  presents  a  plan  for  the  systematic  examination  of  liquid  urine, 
urinary  deposits,  and  calculi.     It  is  compiled  with  the  intention  of  supplying  a 
concise  guide,  which,  from  its  small  compass  and  tabulated  arrangement,  renders 
it  admirably  adapted  for  use,  both  as  a  bedside  reference-book  and  a  work-table 
companion.     The  author  is  well  known  as  one  who  has  had  for  several  j^ears  a  very 
extended  experience  as  a  teacher  of  this  important  branch  of  physical  diagnosis,  and 
lie  has  compiled  a  manual  which  will  serve  to  lessen  the  difficulties  in  the  way  of 
thd  beginner,  and  save  valuable  time  to  the  practitioner. 

THE    MICROSCOPIST'S    ANNUAL  FOR   1879 

Contains  a  list  of  all  the  microscopical  societies  in  the  country,  with  names  of 
officers,  days  of  meeting,  &c.;  alphabetical  and  classified  lists  of  all  the  manufac- 
turers of  microscopes  and  objectives,  dissecting  apparatus,  microscopic  obje3ts, 
materials  for  microscopists,  «fec.,  in  Europe  and  America;  postal  rates,  rules  and 
regulations,  prepared  expressly  for  microscopists.  Weights  and  measures,  with 
tables  and  rules  for  the  conversion  of  different  measures  into  each  other;  customs 
dnties  and  regulations  in  regard  to  instruments  and  books;  value  of  the  moneys  of 
all  countries  in  United  States  dollars;  value  of  the  lines  on  Nobert's  test-plates ; 
t:ible  of  Holler's  probe-platte,  with  the  number  of  lines  to  inch  on  the  several 
diatoms,  &c.;  focal  value  of  the  objectives  of  those  makers  who  number  their 
objectives  (Hartnack.  Nachet,  &c.);  focal  value  of  tlie  eyepieces  of  different  makers; 
magnifying  power  of  eyepieces  and  objectives,  &c  The  whole  forming  an  indis- 
pensable companion  for  svery  working  microscopist.—  Limp  cloth,  gilt.      25  cents. 

A  BOOK  ABOUT  BOOKS;  or,  Practical  Notes  on  the 
Selection,  Use,  and   Care  of  Books. 

Intended  as  a  popular  guide  for  bookbuyers,  students,  and  all 

lovers  of  good  reading. —  Cloth 40  cents. 

This  is  a  readable,  gossipy  book,  full  of  literary  anecdotes,  and  containing  also 
a  great  deal  of  practical  information,  useful  to  every  one  that  owns  or  expects  to 
own  books.  The  directions  for  binding,  repairing,  preserving,  and  handling  books, 
should  receive  the  careful  attention  of  every  one  that  desires  to  keep  his  books  in 
sood  condition ;  but  even  if  regarded  as  mere  ]tleasant  reading  for  a  leisure  hour, 
tliere  are  few  more  readable  and  interesting  books  than  this,  witli  its  gossip,  chat, 
and  stories.  It  is  illustrated  with  three  full-page  engravings,  one  being  a  reproduc- 
tion of  the  first  wood  engraving  of  which  there  is  any  record;  the  second  is  an 
exceedingly  curious  woodcut  representing  the  birth  of'  Eve ;  and  the  third  is  an 
engraving  of  one  of  the  curious  "hornbooks"  of  the  seventeenth  centuiy. 

RHYMES  OF  SCIENCE:   WISE  AND  OTHERWISE. 

By  Oliver  Wendelli  Holmes,  Bret  Harte,  Ingoldsby,  Prof.  Forbes,  Prof. 
J.  W.  McQ.  Rankine,  Hon.  R.  W.  Raymond,  and  others.— With  illustrations. 
Cloth,  gilt  title 50  cents. 

THE  YOUNG  SCIENTIST.— Tins  journal  was  devoted  to  amateur 
Science  and  Art,  and  was  deservedly  a  favorite  with  young  people.  We  have  a 
few  bound  volumes  for  sale.     Pnce  75  cents  each. 

THE     AMERICAN     JOURNAL     OF    MICROSCOPY. 

A  few  bound  volumes  for  sale.    Price  $1  each. 


IMPORTANT    ANNOUNCEMENT 

TO  AECHITECTS,  CONTRACTORS  AND  BUILDERS. 

For  many  years  past  there  has  been  a  want  by  the  building  fraternity  of  a  good 
and  reliable  book  on  Estimating,  one  that  will  give  prices  of  materials  and  labor 
lor  every  department  of  building,  so  far  as  this  is  possible.  Such  a  book,  the  pub- 
lishers believe,  has  at  last  been  produced,  and  is  now  offered  to  those  interested. 

THE  BUILDER'S  GUIDE, 

AND  ESTIMATOR'S  PRICE  BOOK. 

By    FRED.    T.   IIODGSOIV. 

HANDSOMELY  BOUND  IN  CLOTH,  GILT  TITLE.  PRICE,  -  $2.00. 
Current  Prices  of  Lumber,  Hardware,  Glass,  Plumbers'  Supplies,  Paints, 
Slates,  Stones,  Limes,  Cements,  Bricks,  Tin  and  other  Building  Materials; 
also,  Prices  of  Labor,  and  Cost  of  Performing  the  Several  Kinds  of  AVork 
Ilequired  in  Building'.  Together  with  Prices  of  Doors,  Frames,  Sashes, 
S  J  airs.  Mouldings,  Newels,  and  other  Machine  \Vork.  To  Avhich  is  appended 
a  1  irge  nvimber  of  Building  Rules,  Data,  Tables  and  Useful  Memoranda, 
Avith  a  Glossary  of  Architectural  and  Bviilding  Terms. 

Tliis  is  an  entirely  new  work,  and  gives  Prices  of  Labor  and  Materials  down 
to  a  recent  date,  and  is,  therefore,  the  most  reliable  book  in  the  market  on  the 
subject  of  prices  of  labor  and  materials  required  for  building-.  The  work  con- 
tains, besides  Prices,  Data,  Rules,  and  Several  Hundred  Tables  and  Hints  on 
Building,  a  blank  column  where  the  prices  of  Labor,  or  Material  may  be  written 
in  pencil,  where  such  prices  differ  from  those  given  in  the  book.  There  is  also 
a  very  complete  Glossary  of  Building  and  Architectural  Terms  appended  to  the 
work,  which  is  a  useful  and  valuable  addition  for  practical  builders. 

The  work  is  really  a  Cyclopgedia  of  Prices  and  Builder's  Tables,  Data  and 
:Memoranda,  and  is  necessarily  a  large  work,  having  over  330  pages,  each  page 
being  7i  x  4|,  and  covered  with  closely  printed  matter. 

In  order  to  give  an  idea  of  what  the  work  contains,  we  give  the  following  brief 
SY]\OI»SIS    OF    CO.lfTEIVTS: 

Part  L— Contains  Hints  and  Rules  for  Correct  Estimatino;.— Forms  for  Taking 
Estimates,  Quantities,  Prices,  and  Mannerof  Computation.— General  Memoranda 
of  Items  for  Estimates.— Excavations.— Foundations.— Drains.— Iron  Work.— 
Baths  and  Water  Closets.— Brick  Walls.— Carpenter's  Work.— Joiner's  Work.— 
Mantels,  Grates,  Stove  Fittings,  etc.— Pantry,  Closets,  Kitchens  and  Appurten- 
ances.—Bell  Hanging,  Gas  Fixing  and  Fixtures.— Stairs  and  Staircases.— Roofs, 
(Gutters  and  Conductors.— Porches,  Verandas  and  Fences.— Framing;  Cost  of 
same.— Cost  of  Painting,  Plastering,  Shingling,  Slating,  Tinning,  Finishing, 
(rlazing,  Building  Chimneys,  and  other  Brick  Work.— Rules  for  Measurins;  all 
kinds  of  Hip  and  other  Roofs,  with  Cost  of  same.— Rou^h  Boarding.  Shino'ling, 
Siding,  Laying  Floors,  and  other  Work.— Cost  of  Material  and  Labor  for  Stairs, 
Newels,  Balusters,  Rails,  Doors,  Mouldings,  Sliding  and  Folding  Doors,  Windows 
of  all  kinds.  Blinds,  Wainscoting,  Baseboards,  Finials,  Cresting,  Plumbing,  Floor- 
ing, and  everything  else  used  about  a  Building. 

Part  II.— Contains  an  Extensive  Schedule  of  Builder's  Prices,  for  Digging, 
Shovelling,  Ramming  in  Loose  Earth,  Clay  and  Gravel.— Cost  of  Masonry, 
Rubble,  Hammer-Dressed  Work,  Rough  Rock  Work,  Reveals,  Ashler  Work,  Re- 


SYNOPSIS  OF  CONTENTS  (Continued). 

pairs,  Arches,  Plain  Work,  Rubbed  Work,  Beaded  Work,  Fluting,  Reeding, 
Throating,  Grooving,  Rebating,  Leading  in  Work,  Sunken  Work,  Mortising, 
etc.— Prices  of  all  kinds  of  Native  Stones  per  Cubic  Foot.— Prices  of  Cements; 
Portland,  Rosendale,  Keene's,  Lime  of  Teil,  Lime,  Lath,  Slate,  etc.— Bricklay- 
ing; Price  per  1,000,  Laborer's  Wages,  Prices  of  Bricks  of  Different  Grades,  Cir- 
cular and  Elliptical  Work,  Brick  Paving  of  all  kinds.  Laid  Dry  or  in  Mortar,— 
Drain  Pipes,  Cost  and  QuaUty;  Terra-Cotta  Chimney  Tops,  Cresting,  Tiles  and 
Mouldings,  etc.— Colored  Bricks,  Tuck  Pointing,  Setting  in  Sash  and  Door 
Frames,  Taking  Down  Old  Work,  Rebuilding  wifh  Old  Bricks,  Firebricks,  Tile 
Work,  Quality  and  Prices  of  Bricks  from  Various  Localities,  Prices  of  Peerless 
Brick  Company's  Colored  Bricks,  Colored  Mortars  and  Cements,  Odd-Shaped 
Bricks.— Plasterer  s  Work,  Scaffolding,  Lathing,  Mortars  for  all  kinds  of  Work, 
Cements  for  Walls  and  Ceilings,  Cornices  and  Stucco  Work,  Plaster-of-Paris 
Flower  and  Ornamental  Work,  Kalsomining  and  Washes  of  all  Kinds.— Carpen- 
ter's and  Joiner's  Work  ;  Wages,  Prices  of  Lumber,  Prices  of  Made-up  Stuff  of  all 
Kinds.— Hard-wood  Work,  Nails,  Screws.  Locks,  Butts  and  other  Hardware.— 
Stairs  of  all  Kinds,  Table  for  Finding  the  Run  and  Rise  of  Treads  and  Risers, 
Turned  Work  for  Stairs  and  other  Work.— Painting,  Colors,  Prices  for  Different 
Kinds  of  Work,  Ladders,  Scaffolding,  Tools,  Graining,  Painting  Iron  Work, 
Staining,  Repairing  Old  Work.  Numerical  Work,  Tarnishing,  Lettering,  Oihng, 
Sash  and  Door  Painting,  Mixing  Colors,  Prices  of  Colors,  Miscellaneous  Re- 
marks.—Roofing  Materials  of  all  Kinds,  with  Prices  and  Cost  of  Laying  ;  Bell- 
Hanging  Materials,  Skylights,  Tubs,  Sinks,  Sheet  Iron.  Pumps,  Tanks,  Registers, 
Ventilators,  Wire  Ropes,  and  other  matters  required  in  Building. 

Part  III.— Contains  Rules  for  Builder's  Bookkeeping,  Form  of  Balance  Sheet, 
Rules  for  Measuring  Artificer's  Work,  including  Excavation,  Drains,  Shoring, 
Concreting,  and  Labor  in  General ;  also  Methods  of  Measuring  all  Kinds  of  Ma- 
terials for  Brick,  Stone,  or  Wood  Work.— Elements  of  the  Mechanics  of  Archi- 
tecture, Strength  of  Materials,  Rules  for  Obtaining  Same  ;  Iron,  Wood,  Stone 
and  Brick,  Crushing  Loads  for  Various  Building  Materials,  Columns,  Iron,  Wood, 
Stone.— Tables  for  Computing  the  Strength  of  "Materials,  Factors  of  Safety, 
Rolled-Iron  Beams  and  Girders.— Bricks  and  Brick  Piers,  Terra-Cotta,  Strength 
and  Qualities  of  Cements  and  Mortars,  Fire-Brick,  Colored  Mortars,  Granite  and 
other  Stone. 

Part  IV.— Miscellaneous  Tables.— Weight  of  Iron,  Lead,  Brass,  Copper  and 
Cast  Iron,  per  Foot  Superficial  or  in  Bars  ;  Strength  of  Round  Ropes,  Weight  of 
Boiler  Iron,  AVrought-Iron  Pipes,  Flat  and  Round  Wire  Ropes  for  Elevators.  Iron 
Roofing,  Lead  Pipes,  Nails,  Foreign  Weights  and  Measures,  Force  of  Wind, 
Square  Measure,  Long  Measure,  Equivalents,  Arithmetical  and  other  Signs,  Ex- 
pansion by  Heat,  Force  of  Explosives,  Number  of  Shingles,  Slates,  Tiles  and 
other  Covering  Required  for  100  feet  of  Roofing,  Number  of  Bricks  Required  for 
Given  Wall,  Strength  of  Woods,  Loads  for  Bridges,  Strains  on  Bridges  and 
Trusses,  Specific  Gravities. 

Part  V.— Mensuration  of  Superfices,  Areas  of  Squares,  Cubes,  Triangles, 
Multi-sided  Figures,  etc.;  Measurements  of  Solids,  Cubes,  Cones,  Cylinders, 
Splieres,  etc.;  Squares  and  Cubes  of  Numbers,  Table  of  Spherical  Contents, 
Diameters,  Circumferences  and  Areas  of  Circles,  Board  and  Plank  ;Measure, 
Scantling  Measure,  Wages  Table,  Sizes  and  Capacities  of  Cribs,  Boxes  and  Tanks. 

Part  VI.— Mechanics'  Lien  Laws  of  Alabama,  Arkansas,  Connecticut,  Cali- 
fornia, Colorado,  District  of  Cohunbia,  Delaware,  Florida,  Georgia.  Indiana, 
fowa,  Illinois,  Kansas,  Kentucky,  Maine,  Louisiana,  Massachusetts,  Maryland, 
Mississippi,  Michigan,  Missouri',  New  Jersey,  Nevada,  Nebraska,  New  Hamp- 
shire, North  Carolina,  New  York,  Oregon,  Ohio,  Pennsylvania,  Rhode  Island, 
South  Carolina,  Texas,  Tennessee,  Vermont,  Virginia,  West  Virginia,  Wisconsin, 
Ontario. 

Part  VII,— Schedule  of  Architect's  Charges,  Drawings,  Superintendence,  Per- 
centage on  Public  Buildings.— Architect's  Rules  and  Methods  of  Charging  for 
Services  Rendered.— Leading  Architectural  and  Building  Journals.— Glossary  of 
Architectural  and  Building  Terms.  (This  "Glossary"  covers  some  fifty-seven 
pages,  and  deals  with  over  One  Thousand  Terms  used  in  Architecture  and 
Building). 


AJ  A\/     r%    ^      YO/IA 


